President Biden previously worked to pull the Republican leader to debt limit talks in what was seen as an effort by Democrats to undercut Speaker Kevin McCarthy (R-Calif.).
But McConnell has joined Republican senators in lining up behind the House leader as he presses for steep cuts to domestic spending.
And conservatives are pushing him to hold the line.
“If we want to get something done, we’ve got to support Kevin, and then we’ve got to be vocal in what we believe in. It has to come through the Senate; it’s got to take nine of us to pass,” Sen. Rick Scott (R-Fla.) said in an interview.
“I think they’re going to try. I think Biden’s all in to try to do it,” he said.
The push comes after McConnell was met with criticism in his party for working with Democrats more than a year ago to raise the debt ceiling as the nation again found itself not too far removed from the threat of a federal default.
The Treasury warned earlier this month that Congress could have until as early as June 1 to raise the debt ceiling or risk defaulting on its debt.
Biden met with congressional leaders from both sides this week to discuss potential paths forward to raising the debt ceiling after a months-long stalemate.
While leaders said at the time that the meeting produced no significant movement, discussions have continued at the staff level.
“Staff will continue working and all the principals agreed to meet early next week,” a White House official said on Friday.
The Hill’s Alex Bolton has more here.