WASHINGTON — Senate Republicans worked to close ranks Thursday around their leader’s opposition to President Barack Obama picking a new Supreme Court justice, arguing they would be well within their right to refuse to confirm a nominee in Obama’s final year in office.

A day after signs of splintering emerged within the GOP, Republicans mounted a display of unity in the form of a joint op-ed by Senate Majority Leader Mitch McConnell of Kentucky and Senate Judiciary Committee Chairman Charles Grassley of Iowa. Other Republicans walked back earlier comments that had opened the door to granting a hearing and possibly a vote to Obama’s choice to replace Justice Antonin Scalia.

The series of apparent U-turns illustrated the turmoil in the Republican Party about how to handle the unexpected death of Scalia, a conservative stalwart. Obama and Democrats are hoping an overreaction by Republicans will prompt a political backlash that could galvanize support for Obama’s nominee and also invigorate Democratic voters in the November elections.

“No one disputes the president’s authority to nominate a successor to Scalia,” McConnell and Grassley wrote in The Washington Post. But they argued that inconvenient as it may be for Obama, “the Constitution grants the Senate the power to provide — or as the case may be, withhold — its consent.”

Tellingly, the senators didn’t say whether Obama’s nominee should at least get a hearing — just that they’d be justified in refusing an up-or-down vote.

Though most of the GOP’s presidential candidates oppose Obama picking Scalia’s replacement, Florida Gov. Jeb Bush seemed to come to Obama’s defense. He told a CNN town hall that he “probably would” nominate if in Obama’s position.