The House on Monday kicked off its last work week of the year with lawmakers still needing to approve a budget bill to keep the government running after Jan. 15 while softening budget cuts that are squeezing domestic and military spending.

The Senate also returns Monday after a two-week Thanksgiving break to decide on a defense authorization bill and to vote, under newly eased filibuster rules, on one of President Obama's nominees to the U.S. Court of Appeals for the District of Columbia Circuit.

House Speaker John Boehner, R-Ohio, said the House will adjourn Friday with or without a budget agreement, leaving the duty of completing a budget to the Senate, which adjourns Dec. 20.

House and Senate negotiators are hammering out a budget compromise that would keep the government running after the current short-term funding bill expires on Jan. 15. One of the toughest obstacles negotiators face is deciding how to replace billions in sequester-driven budget cuts that would hit all federal agencies starting in January.

House negotiators are zeroing in on a two-year deal that would replace about $65 billion in sequester cuts, mostly by raising governmental fees. The cuts would offset by an increase in airline security taxes, home loan fees and insurance premiums paid by pension funds. The proposal also reduces Medicaid payments to hospitals.

House Republicans and Democrats have limited negotiators' options for offsetting the sequester cuts, giving them few choices beyond raising government fees. Democrats won't tolerate cuts in entitlement programs like Medicare and Medicaid and want to soften the impact of budget cuts on domestic programs. Republicans refuse to consider a tax increase and are concerned primarily with restoring Pentagon funding.

"I think some revenue is appropriate in the mixture as long as you keep those savings," one negotiator, Rep. Tom Cole, R-Okla., told the Washington Examiner.

Lobbyists for the airline industry are warning that negotiators may "double or triple" taxes airline passengers now pay to fund the Transportation Security Administration. The airline fee is technically a tax, but it's not seen that way by Republicans who have refused to support a tax increase. The airline industry is fighting the proposal.

“It’s unreasonable and unnecessary for budget negotiators to be looking to squeeze any more out of an already overtaxed industry and their customers," Nicholas Calio, president of Airlines for America, said in a statement. "We understand the difficulty of the challenge they are trying to meet, but respectfully suggest they look elsewhere to plug the budget hole."

One threat to the budget talks is a Democratic proposal to extend emergency unemployment payments set to expire Dec. 31.

Republicans said they're open to considering extending benefits in the budget bill, though the extension's $26 billion price tag is likely to face opposition from the GOP's rank-and-file members, particularly after the unemployment rate last week fell to 7 percent, the lowest in five years.

Democrats signaled Sunday that they may not insist that the benefits extension be included in the budget deal.

"I don't think we've reached that point where we've said this is it; take it or leave it," Senate Majority Whip Richard Durbin, D-Ill., said on ABC's "This Week."

The Senate this week also will be tackling the 2014 National Defense Authorization Act, which sets policy for the Pentagon. But senators unable to agree on amendments to the bill, including a provision that would implement sanctions on Iran, and may lack the support needed to pass it. The House already passed its version of the bill.

"Time is running short to reach an agreement this year, but it has not yet run out," House Armed Service Committee Chairman Buck McKeon, R-Calif., and the panel's top Democrat, Rep. Adam Smith, of Washington, said in a joint statement.

When the Senate reconvenes Monday, it's expected to move quickly to confirm Patricia Millet to the D.C. circuit court. Millet's nomination has been held up by Republican filibusters that ultimately led to a dramatic Senate rule change barring the use of the filibuster against presidential nominees. Under the new rule, Democrats will easily approve Millet even if all Republican senators oppose her.