Democrats strengthened their hold on the Senate but failed Tuesday to recapture the majority in the House of Representatives they lost two years ago.
President Barack Obama, in his freshly authorized second term, will face the same divided Congress in 2013 that has bedeviled efforts to enact his major legislation.
"Now that the election is over, it's time to put politics aside and work together to find solutions," said Senate Majority Leader Harry Reid, D-Nev., who may have a slightly bigger working majority - but not as big as the filibuster-proof one Obama enjoyed his first two years in the White House.
House Speaker John Boehner, R-Ohio, who also gets to keep his job, offered to work with any willing partner, Republican or Democrat, to get things done. "The American people want solutions - and tonight, they've responded by renewing our majority," he told a gathering of Republicans.
But Boehner also said that by keeping Republicans in control of the House, voters made clear there is no mandate for raising taxes. Obama has proposed imposing higher taxes on households earning over $250,000 a year.
The first post-election test of wills could start next week when Congress returns from its election recess to deal with unfinished business - including a looming "fiscal cliff" of $400 billion in higher taxes and $100 billion in automatic cuts in military and domestic spending to take effect in January if Congress doesn't head them off. Economists warn that the combination could plunge the nation back into a recession.
- Explainer: The 'fiscal cliff" and how it affects you
Because of extreme election-year partisanship, a resolution of the matter had been put off until a post-election lame-duck session. Senate Minority Leader Mitch McConnell, R-Ky., said the voters have not endorsed the "failures or excesses of the president's first term," but rather have given him more time to finish the job.
"To the extent he wants to move to the political center, which is where the work gets done in a divided government, we'll be there to meet him halfway," McConnell said.
Sen.-elect Tim Kaine of Virginia said Wednesday he believes Democrats and Republicans will come together to avoid the "fiscal cliff" threatening the country at year's end.
Kaine, the former governor of Virginia who defeated Republican George Allen Tuesday night, said in an appearance on NBC's "Today" show that voters sent a message to Washington that they want "cooperative government." But he also said the election results show that the public doesn't want "all the levers in one party's hands" on Capitol Hill.
Democrats now hold a 53 to 47 majority, including two independents who generally vote with them. On Tuesday, they held their majority, picking up Republican-held seats in Indiana and Massachusetts while Republicans snatched a lone Democratic seat in Nebraska.
In Maine, independent former Gov. Angus King was elected to succeed retiring GOP Sen. Olympia Snowe. He hasn't said yet which party he will side with - but Democrats rushed to his cause during his campaign. And after Tuesday's victory, Senate Democratic leader Reid reached out to him by phone.
In one closely watched contest, Massachusetts Democrat Elizabeth Warren, a Harvard professor, defeated Republican Sen. Scott Brown, who won the seat in a January 2010 special election following the death of Sen. Edward M. Kennedy. At $68 million, it was one of the most expensive races in the country, even though both candidates swore off money from outside groups. "This victory belongs to you," Warren told supporters at a victory celebration.
In another Democratic pickup, Rep. Joe Donnelly won the Indiana Senate seat held for six terms by Republican Sen. Richard Lugar. Lugar lost earlier this year in a GOP primary to tea party-backed state Treasurer Richard Mourdock. The race had been rocked by the Republican candidate's controversial comments that pregnancy resulting from rape is "something God intended."
And Sen. Claire McCaskill, D-Mo., fought back a challenge from Republican Rep. Todd Akin, who severely damaged his candidacy in August when he said women who are victims of "legitimate rape" would not get pregnant.
Former Virginia governor and Democrat Tim Kaine won the Virginia Senate race, holding off a challenge from Republican George Allen, who lost the seat in 2006. The seat opened up when Sen. Jim Webb, a Democrat, decided not to run for re-election.
And former World Wrestling Entertainment executive Linda McMahon lost her bid for a Connecticut Senate seat to Democrat Chris Murphy despite spending $42 million of her own wealth. It was the second time in two years she has lost a Senate race. The seat had been long held by Sen. Joe Lieberman, an independent who caucused with Democrats and was the Democratic vice presidential candidate in 2000.
In Wisconsin, Rep. Tammy Baldwin defeated former Republican Gov. Tommy Thompson.
In the House, both Boehner and House Democratic Leader Nancy Pelosi of California were re-elected, as were other top leaders of both parties, including House Majority Leader Eric Cantor, R-Va., and the No. 2 House Democrat, Steny Hoyer of Maryland.
And while GOP Rep. Paul Ryan lost the vice presidency, he did win another term to his Wisconsin House seat. Former GOP presidential hopeful Rep. Michele Bachmann of Minnesota was narrowly re-elected.
A party needs 218 seats to control the House. The party mix in the new House will resemble the current one, which Republicans control by 240-190. There are two GOP and three Democratic vacancies. The GOP and Democratic pickups were pretty generally divided.
By early Wednesday, Democrats had defeated 12 GOP House incumbents - 10 of them members of the huge tea party-backed freshman class of 2010. Republican losers included four incumbents from Illinois, two each from New Hampshire and New York, and one apiece from Florida, Maryland, Minnesota and Texas.
But Republicans picked up nine previously Democratic seats. Their candidates defeated one Democratic incumbent apiece in Kentucky, New York, North Carolina and Pennsylvania; they picked up one open seat each in Arkansas, California, Indiana, North Carolina and Oklahoma currently held by Democrats who retired or ran for another office.
With almost 90 percent of the 435 House races called by The Associated Press, Republicans had won 227 seats and were leading in nine more. For a majority in the chamber, a party must control 218 seats. Democrats had won 178 seats and were leading in 19 others.
In remarks to Democrats, Pelosi said her party would be "fighting for reigniting the American dream, building ladders of opportunity for people who want to work hard and play by the rules and take responsibility."
In a somber statement, Sen. John Cornyn, R-Texas, chairman of the National Republican Senatorial Committee, said Republicans "have a period of reflection and recalibration ahead." He added that, "While some will want to blame one wing of the party over the other, the reality is candidates from all corners of our GOP lost tonight."
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(Copyright 2012 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.)