WASHINGTON — Republican efforts to resolve the fiscal standoff that has closed much of the federal government heated up Thursday, the third day of the shutdown, with new talks over a broad budget deal and an effort by more moderate House members to break the logjam.

Representative Paul D. Ryan of Wisconsin, chairman of the House Budget Committee, has initiated conversations with senior House Republicans on a broad deficit reduction deal that would allow some increases to federal programs squeezed by the automatic cuts known as sequestration in exchange for long-term changes to programs like Medicare and Social Security. The package would most likely include instructions to try to move along efforts to simplify the tax code as well.

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.”