* Republicans vow to slash spending, reduce government
* Obama says message is to push harder for common ground
* Republicans pick up 60 in House, 6 in Senate
* U.S. stocks rise 0.4 pct to 6-month high (Adds Cantor quote, stocks)
WASHINGTON, Nov 3 (Reuters) - Exuberant Republicans vowed on Wednesday to exercise their new power in Congress to roll back some of U.S. President Barack Obama's key accomplishments, but a somber Obama said voters wanted both parties to work harder to find common ground.
"It's pretty clear the American people want a smaller, less costly and more accountable government," Republican John Boehner, in line to become the next House of Representatives speaker, told reporters. "Our pledge is to listen to the American people."
Voters, anxious about the economy and unhappy with Obama's leadership, punished Democrats in an election rout on Tuesday that gave House control to Republicans and weakened the Democratic majority in the Senate.
A chastened Obama called the result "a shellacking" and told a White House news conference the solutions demanded by frustrated Americans would be hard to find.
"I'm not suggesting this will be easy," he said. "The overwhelming message that I hear from the voters is that we want everybody to act responsibly in Washington, we want you to work harder to arrive at consensus."
Republicans picked up 60 House seats in the election, knocking Democratic Speaker Nancy Pelosi from power and putting Republicans in charge of House committees. It was the biggest shift in power since Democrats gained 75 House seats in 1948.
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Boehner and Republican Senate leader Mitch McConnell said voters wanted them to roll back the signature initiatives passed by congressional Democrats in the last two years like healthcare and financial regulatory reforms.
But a divided government is more likely to fuel a legislative stalemate when the new Congress begins in January. Senate Democrats can block House initiatives, and Obama's weakened hand will still hold the veto pen.
Top Republicans showed little inclination to compromise.
"We're determined to stop the agenda Americans have rejected and to turn the ship around," McConnell said. "We'll work with the administration when they agree with the people and confront them when they don't."
VOTERS DEEPLY WORRIED
Exit polls found voters deeply worried about the economy, with eight in 10 saying it was a chief concern. Nearly three-quarters believed government did not function properly, and four in 10 said they supported the conservative Tea Party movement of Republicans.
"The people in the heartland, I think it is safe to say, are fearful. They are angry. And they are feeling very strongly that the folks in Washington, in both political parties, just don't seem to get it," said Jim Slattery, a former Democratic representative from Kansas.
The Republican rout extended from coast to coast and knocked more than 30 Democratic incumbents out of the House, including Armed Services Committee Chairman Ike Skelton, Budget Committee Chairman John Spratt and Transportation Committee Chairman James Oberstar.
Obama said he felt "sadness" at the loss of so many Democrats who had taken tough votes to back the healthcare overhaul, economic stimulus package and other initiatives.
"It's hard, and I take responsibility for it in a lot of ways," he said. "There is also a lot of questioning on my part in terms of, 'Could I have done something differently or done something more so that those folks would still be here?'"
Obama said there might be room for agreement with Republicans on areas like natural gas, energy issues and reducing "earmarks" -- local spending projects funded by Congress.
"If the president would like to partner in this effort, I gladly take him up on that offer," Eric Cantor, the No. 2 House Republican, said of the earmarks issue.
Investors said they expected Republicans to be more sympathetic to business concerns. The S&P ended at a six-month high, up 0.37 percent, on Wednesday after the Federal Reserve Board announced plans to aid the economy. [ID:nN03243658]
Boehner said the sweeping healthcare overhaul passed by Democrats in March would ruin the medical system and bankrupt the country. "That means we have to do everything we can to try to repeal this bill and replace it with common sense reforms to bring down the cost of healthcare," he said.
Obama said he did not believe the election was a repudiation of the healthcare overhaul, and he would be willing to work with Republicans on "tweaks." [ID:nN03114576]
Democrats, who have denounced Boehner the past two years as an obstructionist, expressed hope they can now work with him.
'A CONSENSUS GUY'
"We have had a long-standing good relationship. I have found him to be a consensus guy," said Senate Democratic leader Harry Reid, who survived a tough re-election fight in Nevada.
Reid told reporters that Boehner's statements since the election sounded like "the John Boehner that I know, somebody willing to work with us."
Jockeying for congressional leadership has begun. Pelosi was silent about whether she might step down from her leadership post or resign from Congress. The House's No. 2 Democrat, Steny Hoyer of Maryland, is seen as a possible successor.
Republican Representative Mike Pence resigned as conference chairman amid speculation he would mount a presidential bid.
In the Senate, Republicans gained six Democratic seats -- in Indiana, Wisconsin, North Dakota, Pennsylvania and Arkansas as well as Obama's former seat in Illinois. The Senate race in Washington was too close to call.
The three-way race for the Republican-held Alaska Senate seat also was close, with incumbent Lisa Murkowski running as an independent write-in candidate against Tea Party favorite Joe Miller and Democratic challenger Scott McAdams.
The Republican rout extended to governors' races, where they picked up at least 10 governorships from Democrats, including the battleground state of Ohio. They also seized control of at least 17 state legislatures from Democrats. [ID:nN03279028] (Additional reporting by Andy Sullivan, Thomas Ferraro, Richard Cowan and Kim Dixon in Washington, and Angela Moon in New York; Editing by Christopher Wilson and Jackie Frank)