Following the developments today, Boehner said he expected to hear from the president again soon.
"This is the moment, folks," Boehner said. "The fight isn't about numbers; it's about jobs; it's about the future of our country. And we've got a chance to do something big, and we have that chance to do it now. ... For the sake of our economy, the sake for the future of our kids and grandkids, this is a chance and an opportunity that we cannot afford to allow to pass."
Republicans have vowed not to raise the debt ceiling unless a plan to drastically reduce the deficit is attached to the bill.
Heading into negotiations Monday, Cantor declared it was "crunch time" if the group was going to reach an agreement. If Congress fails to pass a bill allowing the federal government to borrow more money, America could default on its debt obligations, a scenario Treasury Secretary Timothy Geithner warned would be "catastrophic."
"The people who would take this to edge, to the brink, they'll own responsibility for calling it to question, our credit worthiness, and that would not be a responsible thing to do," Geithner told ABC News' Christiane Amanpour in April.
Avoiding an economic catastrophe now seems to fall to Obama, Boehner and Senate Majority Leader Harry Reid, D-Nev.
Reid said he had not received an invitation to any formal meetings with the president and speaker.
With Kyl and Cantor gone, the remaining members of the group are Senate Finance Committee Chairman Max Baucus, D-Mont.; Senate Appropriations Chairman Daniel Inouye, D-Hawaii; Assistant House Minority Leader James Clyburn, D-S.C.; and House Budget Committee ranking member Chris Van Hollen, D-Md.
In April, President Obama appointed Biden to lead the bipartisan deficit reduction talks with a group of lawmakers from each of the four caucuses. But as each week has gone by without a deal, lawmakers have been calling on the president to be personally involved in the discussions.
On the Senate floor Thursday morning, McConnell blasted the president for standing in the background.
"Where in the world has President Obama been for the past month?" McConnell asked. "What does he propose? What is he willing to do to reduce the debt and avoid the crisis that is building on his watch?"
Senate Democrats blasted Cantor and Kyl for the breakup of the talks Thursday, and predicted that the negotiations would now fall into the hands of the leadership instead.
"I think it's now, with what Kyl and Cantor's done, I think it's in the hands of the speaker and the president and, sadly, probably, me," Reid said, adding that the Senate's planned August recess is no longer a sure thing.
"I'm terribly disappointed," Reid said of the Republicans' dropping out of the talks. "It appears they're giving up. We can't give up."
With the leadership poised to take over, the days of the so-called Gang of Six-turned- Gang of Five working on economic proposals in addition to the Biden-led formal discussions may be ending.
"My honest feeling is that I think that we're beyond gangs of five and gangs of sixes," Reid said, while noting some progress was made before the talks collapsed. "The Republicans should stop playing chicken and pushing us too close to that line. It's not going to be good for our country or the world."
Boehner said that Republicans are opposed to any tax increases and called on the president to "engage" in order for a deal to be properly worked out.