The offices of Senator Harry Reid, the Nevada Democrat and current majority leader, and Mr. Boehner have been conferring over a lame-duck agenda, with both parties trying to game out what would be to their advantage to dispose of before Republicans take over the Senate and what they can afford to push into 2015.

Leaders of both parties would like to fund the government through Sept. 30 and eliminate any talk of a shutdown for now. Members of the Appropriations Committees favor doing it through a package of new spending bills rather than just funding agencies at current levels. Passing the new bills in a so-called omnibus allows lawmakers to reset agency priorities, but House Republicans have balked in the past at passing such big packages and the leadership may have to settle for a simple extension.

They also have expressed growing interest in trying to pass legislation overhauling the National Security Agency’s once-secret program that is systematically collecting records about Americans’ phone calls. The legal basis for the current call records program, Section 215 of the Patriot Act, will expire in June 2015 without new action.

But because surveillance issues can scramble the usual partisan lines — splitting libertarian conservatives from national security hawks, for instance — it may be in the Republicans’ interest to get the bill out of the way before they assume control of the Senate, avoiding internal discord.

The House of Representatives in May passed a version of the bill, called the U.S.A. Freedom Act, but the Senate has not yet taken up its version, sponsored by Senator Patrick J. Leahy, the Vermont Democrat who leads the Senate Judiciary Committee. In September, James R. Clapper Jr., the director of national intelligence, and Eric H. Holder Jr., the attorney general, endorsed Mr. Leahy’s bill. It also has support from Silicon Valley as well as from the conservative Republican Senators Mike Lee of Utah and Ted Cruz of Texas.

The central element of Mr. Leahy’s bill would get the N.S.A. out of the business of collecting bulk domestic phone records, which it uses to analyze links between people in hope of identifying previously unknown associates of terrorism suspects. Instead, the records would stay in the hands of phone companies, and a new kind of judicial order would permit the government to swiftly obtain calling records of a suspect, along with those of callers up to two links away, even if different companies hold them.

Senate officials are also in negotiations over possible approval of select judicial, executive branch and ambassadorial nominations.

Congressional leaders also want to approve a renewal of the terrorism-risk insurance program and extend a series of business and energy tax breaks, making some of them permanent.