Republicans have complained that Obama has demanded too much in tax revenue and hasn't proposed sufficient cuts or savings in the nation's massive health care programs.
Obama upped the pressure on Republicans to negotiate a fiscal deal, arguing that GOP leaders have rejected his past attempts to strike a bigger and more comprehensive bargain.
"The offers that I've made to them have been so fair that a lot of Democrats get mad at me," Obama said.
Boehner disagreed, saying Sunday that the president had been unwilling to agree to anything "that would require him to stand up to his own party."
Don Stewart, a spokesman for McConnell, said Sunday: "While the president was taping those discordant remarks yesterday, Sen. McConnell was in the office working to bring Republicans and Democrats together on a solution."
The trimmed ambitions of today are a far cry from the upbeat bipartisan rhetoric of just six weeks ago, when the leadership of Congress went to the White House to set the stage for negotiations to come.
"I outlined a framework that deals with reforming our tax code and reforming our spending," Boehner said as the leaders gathered on the White House driveway on Nov. 16.
"We understand that it has to be about cuts, it has to be about revenue, it has to be about growth, it has to be about the future," House Democratic leader Nancy Pelosi said at the time. "I feel confident that a solution may be in sight."
Sen. Dianne Feinstein (D., Calif.) said the 2.1 million Americans whose extended unemployment benefits ran out on Saturday are already feeling the pain of Congress' inaction.
"From this point on, it's lose-lose. My big worry is a contraction of the economy, the loss of jobs, which could be well over 2 million in addition to the people already on unemployment. I think contraction of the economy would be just terrible for this nation. I think we need a deal, we should do a deal," Feinstein said on "Fox News Sunday."
But the deal was not meant to settle other outstanding issues, including more than $1 trillion in cuts over 10 years, divided equally between the Pentagon and other government spending. The deal also would not address an extension of the nation's borrowing limit, which the government is on track to reach any day but which the Treasury can put off through accounting measures for about two months.