WASHINGTON >> Emboldened by a commanding House majority and Senate gains, Republican leaders vowed Wednesday to roll back the size of government and, in time, the nation’s sweeping health care law.

President Barack Obama, reflective after his party’s drubbing, accepted blame for failing to deliver the economic security Americans demand while saying of his health overhaul: “This was the right thing to do.”

He called the election a “shellacking.”

After two years with fellow Democrats leading Congress, Obama now must deal for the rest of his term with the jarring reality of Republican control of the House, a diminished Democratic majority in the Senate and a new flock of lawmakers sworn to downsize government at every chance.

“I’ve got to do a better job,” he said, “like everybody else in Washington.” And he took responsibility for not doing enough to alter the ways of the capital, whether its hyper-partisanship or back-room dealing. “We were in such a hurry to get things done that we didn’t change how things were done.”

Republicans sounded less conciliatory in the first blush of their victories from the midterm elections Tuesday.

“Change course we will,” said Ohio Rep. John Boehner, the speaker-in-waiting, describing the outcome as a clear mandate to shrink the government. That echoed the unrelenting demand of tea party activists whose energy and votes helped to fuel the largest turnover in the House in more than 70 years.

The capital awoke — if it ever slept — to a new political order. With their lopsided win, Republicans are ushering in a new era of divided government and dethroning Speaker Nancy Pelosi, a prime target of their campaign.

Repealing the health care law, with its mandates and subsidies to extend health insurance to nearly all Americans, has been a Republican rallying cry for months but Obama, with his veto power, and the Democrats still in control of the Senate stand in the way. Several Republicans indicated their challenge to the law won’t happen overnight when they take power.

“I think it is important for us to lay the groundwork before we begin to repeal this monstrosity,” Boehner said. Senate Majority Leader Harry Reid, who survived a tea party challenge in Nevada, said “I’m ready for some tweaking” on the health care law but would fight its repeal. Obama, too, indicated he was open to changes, saying Republicans who complain about the burden on small businesses might have a point. But he was not about to see his signature achievement unravel at its core.

In the heady election aftermath, some Republicans cautioned their own that they have work to do in building public trust when many Americans are fed up with both parties.

“We’ve been given a second chance and a golden opportunity,” said Rep. Eric Cantor of Virginia, No. 2 Republican in the House. But, he added, “People want to see results.”

Sizing up the power shift, Reid said he wants to preserve Obama’s health care law and let taxes rise on upper income Americans, but “I’m not bullheaded.”

“If we need to work something out with the people who are really rich, I’ll have to look at that,” he said. “If there’s some tweaking we need to do with the health care bill, I’m ready for some tweaking. But I’m not going to in any way denigrate the great work we did as a country, and saving America from bankruptcy because of the insurance industry bankrupting us.”

The Republican Senate leader, Mitch McConnell of Kentucky, sounded anything but humble in declaring “we are indeed humbled and ready to listen.” At a news conference with Boehner, McConnell said Republicans will cooperate with the other side to the extent Democrats “pivot in a different direction.” He predicted enough Democrats may support the GOP on spending and debt matters to achieve action on that front.

Obama called Boehner to congratulate him late Tuesday. He also spoke with McConnell and top Democrats in a series of conversations that reflected the shifting balance of power. Boehner said Pelosi called and “left me a very nice voice mail” when she missed him, and they will speak later.

Incomplete returns showed the GOP picked up at least 60 House seats and led for four more, far in excess of what was needed for a majority. About two dozen races remained too close to call.

Republicans gained at least six Senate seats, and tea party favorites Rand Paul in Kentucky, Mike Lee in Utah and Marco Rubio in Florida were among their winners. Their comeback was aided by independents, who backed GOP candidates for the first time since 1998.

Not all the tea party insurgents won. Christine O’Donnell lost badly in Delaware, for a seat that Republican strategists once calculated would be theirs with ease until her stunning upset victory in the primary.

In Nevada, Reid dispatched Sharron Angle in an especially costly and contentious campaign in a year filled with them.

The GOP also wrested 11 governorships from the Democrats, Ohio, Pennsylvania and Maine among them, and gave two back, California and Hawaii.