Senate Majority Leader Mitch McConnell and his Republican colleagues have said that they won’t meet with or hold hearings on behalf of the Obama administration’s eventual nominee to replace Antonin Scalia on the Supreme Court, who died last month. But Republicans’ refusal to even negotiate with the Obama administration over who should replace Scalia is not popular with the public at large, according to a poll conducted by the Wall Street Journal and NBC News:

A majority of registered voters disapprove of Senate Republicans’ plans to not hold hearings or consider any Supreme Court nominee from President Barack Obama . . . though the decision has solid support within the party.

The poll, released Tuesday, found that 55% of registered voters disapproved of the decision regarding the opening created by the February death of Justice Antonin Scalia, with some 45% registering strong disapproval.

For more Fortune coverage of Scalia’s death, see:

• Scalia’s Death Just Ignited an Ugly War for the Supreme Court
• 5 Ways Scalia’s Death Will Affect U.S. Business
• What Scalia’s Death Means For Business
• Justice Scalia’s Death: This Changes Everything

It’s a political gambit that could assure the Supreme Court maintains is conservative bent, but one that could also backfire. One concern is that the unpopularity of this strategy will rub off on Senate Republicans in swing states, like Kelly Ayotte, who are facing tough reelection battles. Another problem with the strategy is that a Democrat might get elected to the White House in November, after which the Senate will have less leverage to hold out for a more moderate nominee.