The pair also spoke on Friday, according to a source familiar with the conversation, and another source familiar with the conversation said McConnell delivered the same message to the President that was in the letter.
The House is expected to convene Tuesday to vote on the bill and will have to approve the measure before it can be sent to Biden for his signature.
In his letter Friday, McConnell touted the deal as due to his leadership and blamed the Democrats, namely Senate Majority Leader Chuck Schumer, for the crisis.
“Senator Schumer marched the nation to the doorstep of disaster,” he said. “Embarrassingly, it got to the point where Senators on both sides were pleading for leadership to fill the void and protect our citizens. I stepped up.”
McConnell’s reaction comes after Schumer late Thursday delivered what Democratic Sen. Joe Manchin and several Republican senators sharply criticized as an overly partisan floor speech.
The New York Democrat blamed Republicans in his speech for nearly pushing the nation into default and rebuked their handling of the issue: “Republicans played a dangerous and risky partisan game, and I am glad that their brinksmanship did not work. For the good of America’s families, for the good of our economy, Republicans must recognize in the future that they should approach fixing the debt limit in a bipartisan way.”
In his letter Friday, McConnell called Schumer’s speech “a bizarre spectacle.”
“Senator Schumer exploded in a rant that was so partisan, angry, and corrosive that even Democratic Senators were visibly embarrassed by him and for him,” McConnell said.
CNN reported Thursday that senators on both sides of the aisle reacted negatively to Schumer’s speech.
“I thought it was totally out of line. I thought it was an incredibly partisan speech after we just helped them solve a problem,” said Sen. John Thune of South Dakota, the GOP whip, who had helped find the Republican votes Democrats needed to overcome the filibuster and had voted for it himself despite opposing it. “I let him have it.”
Manchin, a preacher of bipartisanship who tries to bring the parties together on a number of issues, also was unhappy with the tone of Schumer’s speech, which took place on the crowded Senate floor as senators waited to cast the final vote on the debt ceiling extension.
“I don’t think it was appropriate at this time,” the West Virginia Democrat said. “I know Chuck’s frustration has built up, but that was not the way to take it out. We just disagree. I would have done it differently.”
McConnell said his message Friday came “in light of Senator Schumer’s hysterics,” along with reservations about the “partisan spending bill.”
McConnell said Friday that by granting the Democrats more time, it will be up to them to resolve the crisis without his cooperation if the US verges on the brink again.
“I will not be a party to any future effort to mitigate the consequences of Democratic mismanagement. Your lieutenants on Capitol Hill now have the time they claimed they lacked to address the debt ceiling through standalone reconciliation, and all the tools to do it. They cannot invent another crisis and ask for my help,” he wrote.
This story and headline have been updated with additional developments.
CNN’s Manu Raju and Daniella Diaz contributed to this report.