The unexpected death of Supreme Court Justice Antonin Scalia on Saturday reinvigorated an ongoing push among presidential candidates to address how they would handle Court nominations should they be elected.

Saturday night’s Republican presidential debate, hosted by CBS News in South Carolina, took place just a few hours after news broke of Scalia’s death, offering a chance for the GOP to weigh in on the matter. When moderator John Dickerson prompted the candidates to speak about what they thought should happen next, most asserted that the president should not make a new nomination, and instead leave the matter up to his successor.

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Donald Trump fielded the first question on the topic, telling Dickerson that if he were president, he would “certainly want to try and nominate a justice” given the opportunity, but that the Senate should work to block whomever President Obama put forward.

Trump went on to pitch the nominations of conservative federal judges Diane Sykes and Bill Pryor for the vacancy, both of whom have expressed anti-choice sentiments in the past.

Sykes, a judge on the U.S. Court of Appeals for the Seventh Circuit, once sympathized with anti-choice protesters whom she sentenced to 60 days in jail for blocking access to a clinic, saying of those charged, “I do respect you a great deal for having the courage of your convictions and for the ultimate goals that you sought to achieve by this conduct.” Her nomination to the Seventh Circuit Court of Appeals was opposed by a number of reproductive health advocates, including NARAL Pro-Choice America, the National Abortion Federation, Planned Parenthood Federation of America, and the Religious Coalition for Reproductive Choice.

Pryor is a judge for the U.S. Court of Appeals for the 11th Circuit. As Gabriel Roth explained for Slate, Pryor’s appointment to the federal appeals court was originally blocked by Senate Democrats, “who cited his description of Roe v. Wade as ‘the worst abomination in the history of constitutional law,’” before George W. Bush subsequently “installed him in a recess appointment, bypassing the confirmation process.”

Trump has so far refused to say outright whether he would only nominate judges to the Supreme Court who would overturn Roe v. Wade, though he has argued that the landmark Supreme Court decision left the country “sliding toward a culture of death.”

The death of Scalia has also prompted Trump to speculate about the conspiracy theories being popularized by some conservative media outlets. On Monday, the host of radio show The Savage Nation alleged in an interview with Trump that Scalia’s death happened “under suspicious circumstances,” asking Trump whether he thought the justice had been “murdered.” Trump responded that while he couldn’t provide a definitive answer to whether he thought Scalia was murdered, he had “just heard” that “they found a pillow on [Scalia’s] face, which is a pretty unusual place to find a pillow.”

As Vox explained, “While the circumstances of Scalia’s death were somewhat unusual—he was pronounced dead over the phone—there’s little out of the ordinary about a 79-year-old man whose doctor reportedly said he had ‘several chronic conditions’ dying in his sleep.” Vox also pointed out that further reporting suggested the pillow was between Scalia’s head and the headboard.

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The primary concern of Sen. Ted Cruz (TX) when it came to Scalia’s death was that it could endanger abortion restrictions across the country. “We are one justice away from a Supreme Court that will strike down every restriction on abortion adopted by the states,” Cruz told viewers at the debate. 

“The Senate needs to stand strong and say we’re not going to give up the U.S. Supreme Court for a generation by allowing Barack Obama to make one more liberal appointee,” Cruz added.

Cruz had noted his belief that Scalia should be replaced by the next president in a tweet earlier that night, in which he called Scalia an “American hero” and claimed that “we owe it to him” to ensure that Obama doesn’t decide who is nominated for the Court.

Following the debate, Cruz claimed that Trump could not be trusted to pick a Supreme Court justice. An ad released Monday by the Cruz campaign titled “Supreme Trust” featured footage of Trump in a 1999 interview on Meet the Press in which he called himself “very pro-choice.” The ad warned, “We cannot trust Donald Trump with these serious decisions” on “life, marriage [and] religious liberty.”

That same day, Cruz vowed when speaking with reporters in South Carolina to make the 2016 presidential election a “referendum” on the Supreme Court, claiming, according to Politico, that “Donald said his extreme, abortion-supporting sister [Maryanne Trump Barry, a judge on the U.S. Court of Appeals for the Third Circuit] would make a terrific Supreme Court Justice. If the people of South Carolina care about their constitutional rights, we’re one justice away from the Supreme Court writing the Second Amendment out of the Bill of Rights.”

Trump had already told ABC’s This Week on Sunday that he had been joking when he said last August that his sister would be a “phenomenal” choice for the Court, noting that it was “obviously a conflict” of interest for him.

Cruz has made a point of campaigning on a promise to nominate conservative justices to the Supreme Court. “Unlike the very fine individuals on that debate stage, I will be willing to spend whatever political capital is necessary, and sir I give you my word, every justice I put on that court will be a principled constitutionalist jurist with a proven record who will be faithful to the law and will not legislate from the bench,” Cruz said at a January campaign stop in Iowa, according to ThinkProgress.

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During the debate, Ohio Gov. John Kasich said he wished “we hadn’t run so fast into politics” after the justice’s death, but nevertheless continued that Obama “should not move forward” with a nomination for replacement.

“I really wish the president would think about not nominating somebody. If you were to nominate somebody, let’s have him pick somebody that’s going to have unanimous approval, and such widespread approval across the country that this could happen without a lot of recrimination,” said Kasich. “I don’t think that’s going to happen, and I would like the president just to for once here put the country first.”

Earlier that evening, Kasich had released an initial statement on Scalia’s death that took no stance on whether Obama should nominate a replacement, instead focusing on what he deemed a “serious loss to our nation and the Court.”

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Sen. Marco Rubio’s (R-FL) statement at the debate on Scalia’s passing also expressed condolences. Rubio has noted before that it is the “next president” who should nominate Scalia’s successor, a claim that Rubio reiterated later during the debate.

“I do not believe the president [Obama] should appoint someone,” said Rubio. “And it’s not unprecedented. In fact, it’s been over 80 years since a lame-duck president has appointed a Supreme Court justice.”

PolitiFact later rated Rubio’s assertion that Obama’s nomination would lack precedence “mostly false,” explaining that President Ronald Reagan had nominated Justice Anthony Kennedy during Reagan’s second term and confirmed Kennedy during Reagan’s final year in office.

Rubio told the Christian Broadcasting Network in December that nominating judges to the Supreme Court will be “one of the biggest things the next president is going to do,” elaborating that the Court would need justices who understood that “there is no way that you can read that Constitution and deduce from it that there is a constitutional right to an abortion.”

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Former Florida Gov. Jeb Bush dismissed the notion during the debate that it wasn’t within Obama’s rights to pick a new member of the Court. “Of course, the president … has every right to nominate Supreme Court justices,” Bush said.

However, Bush expressed doubts that the president could find a replacement who would be approved by the consensus in the Senate.

“I’m an Article II guy in the Constitution,” Bush said, referencing the portion of the document that grants a president executive power. “We’re running for the president of the United States. We want a strong executive for sure. But in return for that, there should be a consensus orientation on that nomination, and there’s no doubt in my mind that Barack Obama will not have a consensus pick when he submits that person to the Senate.”

Bush doubled down on that stance Sunday during an appearance on CNN’s State of the Union. Speaking with network host Dana Bash, Bush again acknowledged that the president was fully within his rights to nominate a justice at any point during his term. “That’s his prerogative, he has every right to do it,” the presidential candidate said, before noting that “the Senate has every right to not confirm that person.”

“Given his choices of Supreme Court justices in the past, the Senate of the United States should not confirm someone who is out of the mainstream,” Bush concluded.

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While Democrats expressed their condolences upon learning of the death of Scalia, they also condemned members of the GOP for claiming it would be inappropriate for Obama to move forward with nominating a new justice.

“My thoughts and prayers are with the family and friends of Justice Scalia as they mourn his sudden passing. I did not hold Justice Scalia’s views, but he was a dedicated public servant who brought energy and passion to the bench,” said Hillary Clinton in a Saturday evening statement.

“The Republicans in the Senate and on the campaign trail who are calling for Justice Scalia’s seat to remain vacant dishonor our Constitution. The Senate has a constitutional responsibility here that it cannot abdicate for partisan political reasons,” continued Clinton’s statement. 

Later that night, Clinton elaborated, addressing GOP legislators’ intention to block or delay a Supreme Court nominee. “Barack Obama is president of the United States until Jan. 20, 2017, and that is a fact, my friends, whether the Republicans like it or not,” Clinton told the crowd while speaking at a Democratic dinner in Denver, Colorado, according to the Huffington Post. “Elections have consequences.”

“Some might say that a confirmation process would take too long for this president to complete during his remaining days in office,” said Clinton. “But the longest successful confirmation in the past four decades was Clarence Thomas, and that took roughly 100 days,” she continued, pointing out that the president has substantially more time than that left in office.

Speaking in East Las Vegas, Nevada on Sunday, Clinton discussed the importance of appointing a new justice given that the Court has agreed to review the case against Obama’s expansion of the Deferred Action for Childhood Arrivals (DACA) and Deferred Action for Parents of Americans (DAPA) program.

“In the Supreme Court, because of his passing, there will most likely be a tie, four-to-four, on important issues that affect so many people in our country. And the most important is the decision about President Obama’s actions” under these programs, Politico reported Clinton as saying.

“In the case of the decision regarding DACA and DAPA, if there is no new justice appointed, then as with other cases before the court, the decision that was decided will stay in place” in the case of a tie, the former secretary of state continued, referring to the Fifth Circuit Court of Appeals’ decision to pause Obama’s actions on immigration. “And that was a bad decision, I disagreed with it, I don’t think it was the right legal interpretation, I believe President Obama had the authority to do what he did.”

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“While I differed with Justice Scalia’s views and jurisprudence, he was a brilliant, colorful and outspoken member of the Supreme Court,” Sen. Bernie Sanders (D-VT) said Saturday in a brief statement expressing his condolences to Scalia’s loved ones. “My thoughts and prayers are with his family and his colleagues on the court who mourn his passing.”

Later that night, Sanders joined Clinton in criticizing Republicans for speaking out against the president’s intent to nominate a replacement for Scalia.

“It appears that some of my Republican colleagues in the Senate have a very interesting view of the Constitution of the United States,” Sanders said in Denver, according to an ABC News report. “Apparently they believe that the Constitution does not allow a Democratic president to bring forth a nominee to replace Justice Scalia. I strongly disagree with that.”