Count Sen. John McCain among those who believe the U.S. Senate should block any nominee that President Barack Obama attempts to appoint the U.S. Supreme Court to replace Justice Antonin Scalia, who died over the weekend in Texas.

“The president can nominate who he wants to,” McCain said during an appearance today on Mike Broomhead’s Phoenix radio show. “I believe we should wait until after the next election and let the American people pick the next president and we should consider who the next president of the United States nominates.”

Congresswoman Ann Kirkpatrick (D-CD1), who is running for McCain’s seat this year, pounced on McCain’s announcement.

“Members of the U.S. Senate have an obligation to uphold the Constitution and fulfill their duties, including voting on Supreme Court nominees—regardless of party affiliation,” Kirkpatrick told the press via a prepared statement. “John McCain used to take that responsibility seriously. Unfortunately, his comments today show just how much he has changed after more than three decades in Washington. Now is the time to put politics aside and do the right thing for our nation. I urge my colleagues in the Senate to live up to their oaths to the American people and hold up-or-down votes on any nominees put forward.”

McCain himself has generally supported giving a president a lot of leeway when it comes to appointing justices. Kirkpatrick cited McCain’s votes in favor of Clinton appointees for Justice Breyer and Justice Ginsberg, as McCain himself explained in 2005, “because I believed that President Clinton won the election.” And during a battle over whether the Senate should do away with the filibuster of federal judges, McCain was a member of the “gang of 14” that sought to preserve the power of the minority to block judicial appointments because he believed it was important to the political norms and the institution of the Senate.

At the time, McCain told MSNBC Hardball host Chris Matthews: “I strongly believe that the president’s nominees deserve an up- or-down vote and that there was an abuse of that power, and we need to fix that. And we need to do it with an agreement where we can all trust one another.”

But this year, McCain is facing a primary challenge from former state lawmaker Kelli Ward, who is hammering him for the various times that he has gone against the wishes of the hard-core conservatives in Arizona. While Ward’s effort to unseat McCain is still considered a long shot—she had less than $260,000 in the bank at the end of the year and she has yet to win over major national groups that might help her like the Senate Conservatives Fund—McCain has been tacking to the right to inoculate himself from Ward’s attacks.