“If . . . the White House is considering this benefit cut, then President Obama has broken faith with seniors and his commitment to keep Social Security out of the deficit debate,’’ according to a statement from the National Committee To Preserve Social Security & Medicare.

Beneath the tough talk, though, were a softer tone and expressions of guarded optimism.

“I think it is more of a political ploy than it is a serious move forward,” House Minority Whip Steny Hoyer, D-Md., said of Boehner’s plan. But he quickly added, “The good news, however, is that Speaker Boehner indicated that the talks are continuing, so he is not disengaging from the negotiations.”

Members of Congress are in a somewhat more somber mood because of the shootings last Friday of 26 people, including 20 children, at an elementary school in Newtown, Conn. Lawmakers crowded the Senate and House floors offering statements of sympathy, and there was a sense that now isn’t the time for harsh rhetoric. Obama canceled a campaign-style trip to Maine on Wednesday, where he’d planned to try to sell his solution to the fiscal cliff.

"The death of those little children was a message to adults – that more is expected of them," said Ross Baker, a Rutgers University professor and an expert on Congress.

“As the president said in Newtown, a tragedy as unfathomable, unimaginable, as what happened in Newtown reminds us of what really matters,” Carney said. “And he certainly believes that it is his responsibility – and the responsibility of everyone here in Washington – to work together to try to do important things for the American people and the American economy. . . . So to the extent that an event like that, as tragic as it is, brings us a little closer together . . . that would be a good thing.”

Boehner agreed. “This is a difficult time for Americans. That’s why we continue to have conversations with the White House,” he said Tuesday. “It’s not a time to put Americans through more stress.”

Lawmakers also are dealing with reality: Poll after poll finds, in strong terms, that Americans are tired of rigid partisanship and want compromise.

Sources in the White House and the speaker’s office say they’re getting close. Obama’s $2.4 trillion proposal offers an equal amount of revenue and spending cuts, but only $800 billion are true cuts. More than $122 billion would come from the change in the Social Security inflation measurement and $290 billion in savings would derive from lower-interest costs on the national debt.

William Douglas contributed to this article.