The death of Supreme Court Justice Antonin Scalia creates a fight over whether President Barack Obama should nominate a replacement or wait for his successor to do so.

The political battle lines were drawn about an hour after the Supreme Court confirmed the 79-year-old justice died Saturday at a luxury resort in West Texas. Key Republicans said the next president, not Obama, should nominate his replacement.

Obama said that he will “fulfill my constitutional responsibilities to nominate a successor in due time.” The White House, however, said on Sunday night in a statement that he would not send a name up to Capitol Hill until after this week’s congressional recess. And when he does, the president expects the Senate to consider the nominee “consistent” with its responsibilities under the Constitution.

In making that vow, Obama he essentially rejected calls to do otherwise by Senate Majority Leader Mitch McConnell, R-Ky., and two of his party’s presidential hopefuls, Sen. Ted Cruz of Texas and Sen. Marco Rubio of Florida.

“There will be plenty of time for me to do so, and for the Senate to fulfill its responsibility to give that person a fair hearing and a timely vote,” Obama said in a statement. “These are responsibilities that I take seriously, as should everyone. They’re bigger than any one party. They are about our democracy.”

McConnell said in a statement after Scalia’s death that “the American people should have a voice in the selection of their next Supreme Court justice. Therefore, this vacancy should not be filled until we have a new president.”

Cruz, running second to the party’s front-runner, Donald Trump, tweeted sentiments similar to McConnell’s.

Justice Scalia was an American hero. We owe it to him, & the Nation, for the Senate to ensure that the next President names his replacement.

— Ted Cruz (@tedcruz) February 13, 2016