Aides described those talks as “conversations about conversations,” not true negotiations, and they favored the term “down payment” on the deficit over “grand bargain.” But the “down payment” that Mr. Ryan is pursuing must come together fast, to provide a framework that Speaker John A. Boehner of Ohio can use to win over enough Republicans to reopen the government and raise the Treasury’s statutory borrowing limit before a government default in two weeks.
“The longer this goes, the closer we get to the debt limit and the more the two of these roll together,” said Representative James Lankford, Republican of Oklahoma and a member of the Budget Committee. “If any agreement is going to happen we’re going to have to have multiple negotiators rather than have Boehner come back with it.”
In a Capitol rattled by a shooting on the grounds that killed a woman and injured a police officer, tempers have flared and pressure appears to be mounting to resolve a stalemate that has shut large parts of the government, sidelined 800,000 federal workers and forced more than one million more to work without pay.
As the shooting incident was still unfolding, Representative Tim Griffin, Republican of Arkansas, took to Twitter to imply a connection with the shots fired outside the Capitol and the heated words inside. “Stop the violent rhetoric President Obama, Chuck Schumer and Nancy Pelosi. #Disgusting,” he wrote, only to delete the message later.
There were signs on Thursday, however, that some lawmakers were willing to work together to end the dispute. About 20 Republicans and Democrats signed on to a proposal that would reopen the government, finance it for six months and repeal the health care law’s tax on medical devices, a provision that has bipartisan opposition.
Representatives Charlie Dent, Republican of Pennsylvania, and Ron Kind, Democrat of Wisconsin, framed it as a compromise that both sides should be willing to accept to reopen the government.
“It’s important that we accept incremental progress when we can,” Mr. Dent said. “What we’re talking about here is leadership.”
Senator Lindsey Graham, Republican of South Carolina, approached Senator Charles E. Schumer, Democrat of New York, to try to open talks, also centered on the medical device tax as a face-saving victory for Republicans looking for a graceful way to back down.
And there has been some softening of the tone on the Republican side. Mr. Lankford, a member of the Republican leadership, conceded the “quandary” he faces in his district.
“Some people like the Affordable Care Act, and like what’s happening with it. Some people really don’t,” he said. “People have two minds as they walk through it.”
President Obama, speaking in a Maryland suburb of Washington on Thursday, tried to keep the heat on Republicans, saying what many in the party freely acknowledge: if Mr. Boehner allowed the House to vote on a spending bill to reopen the government free of any provisions that would undermine the health care law, it would pass with bipartisan support.
“Speaker John Boehner won’t even let the bill get a yes-or-no vote because he doesn’t want to anger the extremists in his party,” Mr. Obama said. If the speaker did so, he added, within minutes “we can get back to the business of governing and helping the American people.”
Certain of their advantage, Senate Democratic leaders said they had no intention of accepting even the modest compromise the House centrists were offering.