WASHINGTON >> A chastened President Barack Obama signaled a willingness to compromise with Republicans on tax cuts and energy policy Wednesday, one day after his party lost control of the House and suffered deep Senate losses in midterm elections.

Obama ruefully called the Republican victories “a shellacking.”

At a White House news conference, the president said that when Congress returns, “my goal is to make sure we don’t have a huge spike in taxes for middle class families.” He made no mention of his campaign-long insistence that tax cuts be permitted to expire on upper-income families, a position he said would avoid swelling the deficit but put him in conflict with Republicans.

He also virtually abandoned his legislation — hopelessly stalled in the Senate — featuring economic incentives to reduce carbon emissions from power plants, vehicles and other sources.

“I’m going to be looking for other means of addressing this problem,” he said. “Cap and trade was just one way of skinning the cat,” he said, strongly implying there will be others.

In the campaign, Republicans slammed the bill as a “national energy tax” and jobs killer, and numerous Democrats sought to emphasize their opposition to the measure during their own re-election races.

The president opened his post-election news conference by saying voters who felt frustrated by the sluggish pace of economic recovery had dictated the Republican takeover in the House.

Asked to reflect on the returns, he said, “I feel bad,” adding that many Democrats who went down to defeat had done so knowing they risked their careers to support his agenda of economic stimulus legislation and a landmark health care bill.

The president said he was eager to sit down with the leaders of both political parties “and figure out how we can move forward together.”

“It won’t be easy,” he said, noting the two parties differ profoundly in some key areas.

One controversial issue, the president said he saw a possibility that Congress might agree to overturn the military’s ban on openly gay service members when lawmakers return to the Capitol for a post-election session later this month.

The election was a humbling episode for the once-high-flying president, and the change showed during his news conference. Largely absent were his smiles and buoyant demeanor, replaced by somberness and an acknowledgment that his policies may have alienated some Americans.

“I think people started looking at all this, and it felt as if government was getting much more intrusive into people’s lives than they were accustomed to,” he conceded. But he wasn’t talking surrender either.

He sought to tread a careful line, suggesting he would cooperate with Republicans where it was possible and confront them when it was not.

“No one party will be able to dictate where we go from here,” he said, a clear warning to Republicans that he won’t simply bow to their demands for a sharply conservative switch in economic policy.

With his comments, Obama largely followed the lead of Republican leaders who said earlier in the day they were willing to compromise — within limits.

With unemployment at 9.6 percent, both the president and the Republicans will be under pressure to compromise. Yet neither must lose faith with core supporters — the Republicans with the tea party activists who helped them win power, Obama with the voters whose support he will need in 2012.

The president said the economy had begun a recovery since he took office but Americans became wary when they saw government bailouts of failing banks and two of the Big Three U.S. automakers.

Many Republicans campaigned by calling for repeal of the health care legislation Obama won from Congress, but the president said repeal was a nonstarter.

“If Republicans have some ideas” for cutting costs of health care or making other changes in the bill, he said he would be glad to take a look.

“There are going to be some examples of where we can tweak and make progress,” he said. “But I don’t think if you ask the American people, ‘should we stop trying to close the doughnut hole that helps seniors get prescription drugs, should we go back to where people with pre-existing conditions can’t get health insurance’ … I don’t think you’d have a strong vote from people saying, ‘Those are provisions I want to eliminate.”‘

Famously unemotional in public, Obama was asked whether he needs to change his leadership style, and he responded: “When you’re in this place, it is hard not to seem removed.”

He said he needs to do more “to ensure I’m getting out of here.” He also pointed out that “a couple of great communicators” — Reagan and Clinton — also stood at the podium two years into their presidencies “getting very similar questions.”

Actually, Clinton’s electoral comeuppance was worse. Republicans won both the House and Senate at his first midterm, but he recovered to win re-election two years later.

Republicans lost seats in Congress at Reagan’s first midterm election in 1982 but never had a House majority to lose, and kept control of the Senate for four more years.