"In the end, we couldn't connect," Boehner wrote Republican rank-and-file lawmakers, accusing the president of wanting to raise taxes and being reluctant to cut benefit programs.
But Obama, in a rare Friday evening turn at the White House podium, said, "I've been left at the altar now a couple of times."
"If Congress and the House Republicans are not willing to ensure that we avoid default, it's fair to say they take responsibility for whatever arises," the president said.
Earlier Friday, the Senate rejected a House plan containing deep spending cuts.
The 51-46 party-line Senate vote left unresolved the urgent issue of how to lift the nation's borrowing powers to avoid a first-ever U.S. default on Aug. 3.
The Senate vote against the tea party-backed measure had been expected in the Democratic-run chamber.
"There was no agreement, publicly, privately, never an agreement, and frankly not close to an agreement," Boehner said.
Obama has asked bipartisan congressional leaders to meet at the White House on Saturday morning to discuss the way forward on a deal to boost the nation's borrowing authority.
Obama called for the meeting after Boehner told the president he was walking away from the talk.
Obama says he will meet with Boehner, Senate Republican leader Mitch McConnell, House Democratic leader Nancy Pelosi and Senate Democratic leader Harry Reid. Obama says time is running out to reach a deal by Aug. 2 to avert a default.
The administration says if the debt ceiling is not raised by Aug. 2, the government is in danger of defaulting for the first time in its history.
During a town hall meeting at the University of Maryland, Obama stressed that the U.S. has never defaulted on its debt and won't do so now.
"The United States of America doesn't run out without paying the tab. We pay our bills. We meet our obligations," Obama said.
The Associated Press contributed to this story.