A conservative legal group is looking to stiffen the spines of Senate Majority Leader Mitch McConnell (R-Ky.) and swing-state Republican senators in the upcoming fight over replacing the late Justice Antonin Scalia on the Supreme Court.

The Judicial Crisis Network announced a seven-figure advertising campaign aimed at pressuring McConnell and six other senators to hold off on any aspect of considering a replacement for Scalia until after President Obama leaves office. Though McConnell has declared that Scalia’s seat on the bench should not be filled “until we have a new President,” there has been some disagreement among Republicans over whether the upper chamber should hold hearings and votes on a nominee, who Obama is expected to name in the coming weeks.

The members targeted are Kelly Ayotte (N.H.), Chuck Grassley (Iowa), Ron Johnson (Wis.), John McCain (Ariz.), Rob Portman (Ohio) and Pat Toomey (Pa.).

A 30-second television ad titled “Let the People Decide” will run in Washington, D.C. during the Sunday political talk shows and in senators’ home media markets, the group announced. The ad buy includes radio and digital campaigns in addition to TV content.

“We want to thank the U.S. Senators who say that the American people should decide who picks the next Supreme Court justice.  The American people are fed up with Washington politicians, and the selection of the next justice is simply too important to leave to politics as usual,” Judicial Crisis Network Chief Counsel Carrie Severino said in a statement.

The group sees high stakes for the conservative movement in 2016 when it comes to the Supreme Court. One television spot that ran during a Republican presidential primary debate last year implicitly criticized Chief Justice John Roberts, who became persona non grata on the right after ruling to uphold the Affordable Care Act in 2012. “We can’t afford more surprises,” the ad stated, showing a photo of Roberts.

The advertising campaign announced Thursday is the latest development in a brewing political fight over how and when to confirm a replacement for Scalia, 79, who was pronounced dead at a West Texas ranch on Saturday.

At issue is whether the Senate should ignore any Supreme Court candidate nominated by Obama or at least hold hearings and potentially votes on a possible Scalia replacement. There is little doubt that any nominee would be rejected by the Republican-controlled Senate, but some conservatives worry that any publicity that would accompany hearings could help Democrats build the case that the GOP is obstructing the process.

The unexpected vacancy on the Supreme Court at the height of presidential primary season has upended the political debate, as Republican candidates seize the moment to boost their conservative credentials and Democrats paint the GOP as being unreasonable and unwilling to govern.

The Judicial Crisis Network advertisements highlight pressure from the right on senators who the conservative base does not trust to maintain a strong position against confirming a new justice before November. The television ad urges voters to “thank” senators for “letting the people decide” by calling their offices. The message to the members is clear: stick with us, or there will be trouble.

As chairman of the Judiciary Committee, Grassley has declined to rule out hearings, saying he won’t make a decision until Obama makes a nomination.