Every issue in dispute remains unresolved, waiting to be addressed when Congress returns next month for an election-year session in which agreements could be even more elusive.
Basically, the new law, signed on Friday by Mr. Obama, preserves the status quo through February, so House and Senate negotiators can try to reach longer-term agreements on the Social Security payroll tax, unemployment insurance, Medicare and a few other issues, like the shape of the welfare program that provides cash assistance to more than 4.6 million poor people.
The law says that Mr. Obama shall grant a permit within 60 days for construction of the Keystone XL oil pipeline, from Canada to the Gulf Coast, unless he finds that the project “would not serve the national interest.” Republicans in Congress are already looking for additional ways to put pressure on Mr. Obama if he blocks the pipeline or delays a decision.
Under growing political pressure, House Republican leaders accepted the two-month extension of payroll tax relief. But many rank-and-file members of the House Republican caucus said they doubted that the tax break would do much to stimulate the economy and saw no urgent need to continue it for 10 more months. By contrast, Mr. Obama and Congressional Democrats say the payroll tax cut is needed to bolster the economy.
An extension of the tax cut and jobless benefits “should be a formality,” Mr. Obama said. But he added, “We have a lot more work to do,” and said he expected “some tough fights.”
Even if Democrats and Republicans could agree on extending the payroll tax cut, they fundamentally disagree about how to offset the additional cost, $100 billion for the last 10 months of 2012.
The Senate majority leader, Harry Reid of Nevada, made clear on Friday that Democrats would keep pressing for a tax surcharge on individual income over $1 million — a demand dropped by Democrats in talks that led to the two-month compromise.
“There should be a fair tax on rich people,” Mr. Reid said.
With a few exceptions, Republicans in Congress have opposed a “millionaires’ tax,” saying it would hurt the economy and people who create jobs.
House Republicans would pay for the legislation, in part, by freezing the pay of federal employees through September 2013.
Democrats generally oppose that idea.
A 20-member conference committee will try to work out differences between the House and the Senate on a yearlong bill. Mr. Reid said he had appointed Senator Benjamin L. Cardin of Maryland to the panel because he knew that Mr. Cardin would guard the interests of federal employees. More than 275,000 federal workers live in Maryland.
The fate of the main federal-state welfare program, Temporary Assistance for Needy Families, was largely overlooked in the fight over payroll taxes. Money and the legal authority for the welfare program were due to run out on Dec. 31.
Jennifer Hrycyna Wagner, the welfare director in Illinois, said state officials around the country feared a possible interruption in benefits and services for “our most vulnerable residents.”
Congress extended the program for two months, but its future beyond that is up in the air. If Congress provides additional welfare money, it is likely to come with new conditions.
Many states deliver cash assistance using electronic benefit transfer cards. The House has voted twice this month to forbid use of the cards at any liquor store, casino or strip club — any “retail establishment which provides adult-oriented entertainment in which performers disrobe or perform in an unclothed state for entertainment.”
Several states have been embarrassed by the disclosure that welfare recipients were claiming benefits at such places.
Representative Gwen Moore, Democrat of Wisconsin, opposed the restriction, saying it would “humiliate and marginalize” poor people.
“In many neighborhoods,” she said, “the closest A.T.M. is located in a nearby liquor store.”
Some state officials also question the provision. Miki Allard, a spokeswoman for the Nevada Department of Health and Human Services, said: “It may be very appropriate for our public assistance recipients to access benefits from casino machines. A large proportion of our clients work in casinos. They are not there to gamble. They are there to work.”
A bigger fight looms over unemployment insurance. House Republicans want to reduce the maximum duration of benefits to 59 weeks, from 99. They would allow states to require drug testing. And they would require most recipients of jobless benefits to search for work and to enroll in G.E.D. programs if they had not completed high school. Republicans also want to allow waivers of federal law so some states could divert money from the payment of benefits to the retraining of workers. Democrats oppose most of those ideas, saying they would cut a lifeline for millions of people who have been out of work for a year or more.
Senator Jack Reed, Democrat of Rhode Island, will be a member of the House-Senate conference committee. In picking him, Mr. Reid noted that Rhode Island had high unemployment and said “no one in the Senate has been more protective of the unemployed.”
The negotiators will also try to find a new way to pay doctors treating Medicare patients, to avoid the continual threat of deep cuts in fees.
Unless Congress steps in, doctors will see a 27 percent reduction in Medicare reimbursements in March. As a result of such cuts, lawmakers say, many older Americans could lose access to their doctors, because doctors would be less willing to take Medicare patients.
One of the five House Democrats named to the conference committee, Representative Allyson Y. Schwartz of Pennsylvania, is drafting legislation to scrap the current payment formula, which penalizes doctors if Medicare spending on physician services exceeds annual goals linked to growth of the nation’s economy.