Read more of our articles on Justice Antonin Scalia’s potential successor here.

GOP senators up for re-election in battleground states face an uphill battle to retain their seats thanks to their insistence on blocking anyone President Obama nominates for the Supreme Court.

Polling released this week from Public Policy Polling found that residents of many states with competitive Senate races support filling the vacant seat on the Supreme Court left by the death of Justice Antonin Scalia. These polls suggest voter opinions are in direct conflict with the vow made by Senate Majority Leader Mitch McConnell (R-KY) to obstruct any candidate nominated to replace Scalia.

In New Hampshire, where Sen. Kelly Ayotte is running for re-election, 59 percent of voters support filling the vacant Supreme Court seat. Similar levels of support have been found in other states with contentious Senate battles: in Wisconsin, 62 percent of voters support filling the vacancy, as do 58 percent in Ohio, and 57 percent in Pennsylvania.

The polls found that the majority of respondents in all of these states said they were less likely to vote for their Republican senators because of their refusal to consider a nominee for the Roberts Court.

Ayotte faces a tough campaign against New Hampshire Gov. Maggie Hassan (D) for U.S. Senate, but has nonetheless pledged to obstruct any candidate put forth for the Court.

“We’re in the midst of a consequential presidential election year, and Americans deserve an opportunity to weigh in given the significant implications this nomination could have for the Supreme Court and our country for decades to come,” Ayotte said after Scalia’s death, according to Politico. “I believe the Senate should not move forward with the confirmation process until the American people have spoken by electing a new president.”

Sen. Rob Portman (R-OH), who is running against Democratic candidate and former Ohio Gov. Ted Strickland, promised not to even meet with Obama’s choice. “Not if we’re not going to move forward,” Politico reported Portman said about the Republican majority blocking an Obama nominee.

“Why not let the American people also decide the direction of the Supreme Court?” Sen. Ron Johnson of Wisconsin asked during an NPR interview last week. “I realize the voters elected President Obama in 2012, but they also, in 2014, elected enough Republican senators to gain a majority in the Senate so we control the confirmation process …. But not acting is also acting.”

Sen. Pat Toomey (R-PA) said in a statement to the New York Times that “The next Court appointment should be made by the newly-elected president. President Obama insists that he will nominate someone for the Court. He certainly has the authority to do so. But let’s be clear—his nominee will be rejected by the Senate.”