Here are some of the major issues and how they are likely to fare in the world of divided government:
Taxes. Bush-era tax cuts expire at the end of the year. The lame-duck Congress soon will try to find a compromise to extend the tax breaks. Republicans want all of them to stay in place, while Obama would like to keep the tax cuts in place for the middle class but let them expire for the wealthiest Americans. Many analysts expect Obama will agree to extend all of them for a year or so.
The estate tax also might get a short reprieve. Because of disagreements in Congress, the tax on inheritance expired this year. Starting next year, it is scheduled to go into effect at high rates on estates valued at more than $1 million. Congress is likely to push the issue off until next year and then reinstitute the tax, but with a larger exemption than in recent years — such as no tax on the first $3.5 million per person, said David Gergen, an adviser to Clinton and several GOP presidents and director of the Center for Public Leadership at the Harvard Kennedy School. The uncertainty has been hard on many senior citizens, Gergen said.
Deficit, Social Security, spending and jobs. A bipartisan presidential commission is expected to report by year's end on how to tackle the ballooning deficit. Both Obama and Republican leaders have said the issue is crucial. Public opinion polls show voters agree.
But actually getting anything done is difficult. Republicans generally refuse tax increases as part of the solution, and Democrats usually fight against benefits and spending cuts.
"If you're going to get a change on this, someone is going to have to take a big political risk," said Al From, who created the centrist Democratic Leadership Council.
Republicans have vowed to cut spending to reduce the size of government, starting with a rollback to 2008 levels. That makes it unlikely that Obama will have a chance to pass another large-scale stimulus package to try to create jobs.
Many of the most-talked-about proposals for dealing with the deficit would have an impact on Social Security, such as raising the retirement age or changing Social Security tax rates.
"It means we'll be under the gun much more than we have been," said Barbara B. Kennelly, president and CEO of the National Committee to Preserve Social Security and Medicare.
Kennelly noted that the probable new chairman of the House Budget Committee, Wisconsin Republican Paul Ryan, favors private accounts for Social Security and vouchers for Medicare.
Health care and Medicare. Republicans minced no words on the campaign trail about how they felt about "Obamacare," the health care reform that broadens the number of people covered by insurance by putting new requirements on businesses, insurance companies and individuals. Many of the people elected Tuesday want the plan repealed.
Rother and others don't expect Republicans to have the votes to override a presidential veto. But they could try to slow down funding for health care reform or pick off small provisions, said James Thurber, director of the Center for Presidential and Congressional Studies at American University.
One piece of health legislation that will come up quickly is the formula used to calculate reimbursement for doctors who treat Medicare patients. If Congress does not act, reimbursement rates for doctors will automatically be cut by 23 percent at the end of the year, according to Rother. That could make it harder for seniors to find available doctors. Rother expects the lame-duck Congress to put the matter off until next year, which would raise the price tag of an eventual solution.
Energy and the environment. Sweeping plans to tackle global warming issues and energy policy are on ice. Obama's so-called cap-and-trade legislation to regulate the greenhouse gases that create climate change was wildly unpopular with the business community.
"Cap and trade is dead for a generation, if not forever in America," said Thurber.
Some environmental measures could be approached through regulatory policy, which Obama still controls. Franc, of the Heritage Foundation, said Democratic efforts to regulate carbon dioxide would have to be done through executive branch rules if Obama wants to have a chance of seeing them happen.
Tamara Lytle is a veteran Washington-based political correspondent.
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