GOP leaders are pressing the party to choose between Trump’s vice presidential pick and his pick to be his health secretary.
Democrats are expected to vote Monday night to send their nominee to the Senate for a confirmation vote, and it could be as early as Tuesday morning if the votes don’t change.
The top Senate Republican, Mike Lee of Utah, said that if the Senate fails to act Monday, the House will vote on a “no” vote on the GOP pick, which he said would be a “travesty of democracy.”
The move came as House Democrats and liberal groups demanded the GOP nominate a woman for the Cabinet post.
But the White House signaled Sunday that the administration would not support a Biden pick.
Trump is a strong supporter of women and has said he would be open to the nomination of any woman for Cabinet positions.
The White House also signaled that it may choose to back the Senate’s choice of Jeff Sessions for attorney general.
Sessions was forced out of the Senate in April, when he faced calls from the Trump administration to step down.
“The president has said in the past that he would not have nominated Jeff Sessions to the position,” White House press secretary Sean Spicer said Sunday on ABC’s “This Week.”
“He has not said that he is going to do that today.
So he’s got a choice, he’s going to say, ‘Hey, I’m not going to confirm him,'” Spicer added.
Spicer also said the administration will not be supporting a nominee from another party.
If the Senate votes to confirm the vice president’s pick, Trump would face the prospect of facing Democratic objections to a nominee that could be a moderate who would push the party further to the right.
Republicans have said the choice would be made on the Senate floor.