Top Republicans have urged Barack Obama to change course after the president's huge setback in mid-term elections.
John Boehner, set to become the next speaker of the House of Representatives, said Americans had voted for "smaller government".
He pledged to repeal Mr Obama's healthcare reform "monstrosity", to cut spending and to create jobs.
Republicans captured 60 seats in the House to take power there, but the Senate remains in Democratic hands.
Mr Boehner vowed to start work on the "people's priorities".
"They want the president to change course. Change course we will," he said.
Mr Boehner insisted that halting the president's flagship healthcare reform was a top priority.
"I believe the healthcare bill will kill jobs, ruin the best healthcare system in the world and bankrupt our country," he said.
"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 health care."
In the Senate, the Republicans made a net gain of at least six seats, leaving the Democrats with a slim majority.
Republican Minority Leader Mitch McConnell said the vote had clearly been a referendum on the Democratic Party's record over the last two years.
Dozens of those House seats and several Senate ones went to candidates backed by the Tea Party conservative anti-tax movement.
The election result is a stinging setback for the president, who was elected only two years ago with so much hope and so much exuberance, says the BBC's North America editor Mark Mardell.
While there will be much talk of compromise and reaching deals, many Tea Party supporters' explicit aim is to block and undo Mr Obama's agenda, our editor says.
Up for election were all 435 seats in the House (the lower chamber of Congress), 37 of the 100 seats in the Senate, governorships of 37 of the 50 states and all but four state legislatures.
With some counts still to be completed, projections suggested the Republicans had obtained a net gain of 60 seats in the House, more than the 54 they won in the landmark 1994 mid-terms, and the biggest exchange of seats since the Democrats won 75 in 1948.
Compounding the misery for Mr Obama's camp, a Republican captured the president's old Senate seat in Illinois.
Republicans also took Senate seats from Democrats in Pennsylvania, Wisconsin, Arkansas, North Dakota and Indiana.
In Arkansas, Republican John Boozman defeated incumbent Blanche Lincoln in a historic reverse for the Democrats.
But in Nevada, one of the most dramatic contests of the night, the Democrats' leader in the Senate, Harry Reid, fought off Tea Party challenger Sharron Angle.
Mr Reid's victory sparked a delighted reaction from Senator John Kerry.
"Harry Reid isn't just Dracula, he isn't just Lazarus, he's our leader and our whole caucus is thrilled that he's unbreakable and unbeatable," he said.
Senate results from Washington State, Alaska and Colorado have still to be called.
'Tea Party tidal wave'
Within the Republican Party, the Tea Party movement celebrated a number of successes.
The movement, backed by former Alaska governor and 2008 Republican vice-presidential candidate Sarah Palin, managed to replace establishment Republican candidates with its candidates in some areas.
Tea Party favourite Rand Paul held Kentucky for the Republicans.
"We've come to take our government back!" Mr Paul said in his victory speech, adding there was a "Tea Party tidal wave".
However, his fellow Tea Party activist and Senate victor in Florida, Marco Rubio, sounded a note of caution.
"We make a grave mistake if we believe tonight these results are somehow an embrace of the Republican Party," he said.
"What they are is a second chance - a second chance for Republicans to be what they said they were going to be not so long ago."
But Christine O'Donnell, seen as a rising star of the movement, lost her Senate bid in Delaware after a campaign mired in controversy about her past life.
Governorships change hands
Republicans took governorships from Democratic hands in at least 10 states, including Pennsylvania, Michigan and Ohio, which is considered a crucial battleground for the 2012 presidential election. They also held Florida, where Democrat Alex Sink conceded victory to Republican Rick Scott after a bruising race.
The Democrats reversed the trend in two states, ousting Republicans in Hawaii and California, where Democrat Jerry Brown returned to the governorship after three decades, cruising past the billionaire former eBay boss Meg Whitman.
In five states, the result was still too close to call.
Among various local referendums, an attempt to legalise marijuana in California was defeated, while Oklahoma backed a measure banning judges from using Islamic law in rulings.