(AP) -- One day after sweeping Republican election gains, President Barack Obama and incoming Senate Majority Leader Mitch McConnell pledged to try and turn divided government into a force for good rather than gridlock on Wednesday, yet warned of veto showdowns as well.

"There is no doubt that Republicans had a good night," the president said at the White House, referring to big gains that left the GOP in control of the Senate, with an expanded House majority and in possession of a handful of governorships formerly in Democratic hands.

To voters who handed the GOP control of Congress, he said, "I hear you. ... It's time for us to take care of business." He cited construction of roads, bridges and other facilities as one area ripe for cooperation. He said expanded trade was another.

At the same time, he noted, "Congress will pass some bills I cannot sign. I'm pretty sure I will take some actions that some in Congress will not like."

Obama and McConnell presented differing profiles at news conferences a little more than an hour apart.

The 53-year-old president now faces a Congress under two-house control by Republicans for the first time in his tenure - and a lame duck status that becomes more of a check on his political power with each passing day.

McConnell, 72 and famously taciturn, smiled and joked with reporters on the day after achieving a lifelong ambition.

Still, the two said they had had a pleasant telephone conversation earlier in the day.

"I would enjoy having some Kentucky bourbon with Mitch McConnell," said Obama.

Said McConnell, " in our system the president is the most important player" who can veto legislation or persuade lawmakers of his own party to back compromise.

Immigration loomed as one early irritant.

Obama said that unless Congress takes action by the end of the year, he will order a reduction in deportations of working immigrants living in the country illegally.

He made his pledge a short while after McConnell warned him against acting unilaterally.

"It's like waving a red flag in front of a bull to say if you guys don't do what I want I'm going to do it on my own," McConnell said at a news conference in Kentucky.

McConnell also cited trade and taxes among areas ripe for compromise.

"There will be no government shutdown or default on the national debt," he said, making clear he doesn't agree with some tea party-backed lawmakers who have supported one or the other in the past - or may want to in the future.

McConnell will take office in January as Senate majority leader, and he and House Speaker John Boehner will have the authority to set the congressional agenda.

Boehner ceded the Republican limelight to McConnell for the day. The Ohio Republican is in line for a third term as House leader - and his first with a Republican majority in the Senate.

At his news conference, McConnell said, "When America chooses divided government, I don't think it means they don't want us to do anything. It means they want to do things for the country."

He cited trade legislation and an overhaul of the tax rules as two areas ripe for agreement.

Beyond that, he made it clear Congress will vote on legislation to approve the Keystone XL oil pipeline from Canada through the United States, and work to repeal portions of the health care law that stands as Obama's signature domestic accomplishment. He said a tax on medical devices and a mandate for individuals to purchase health insurance are also Republican targets.

Obama ruled out ending the requirement for purchasing of health care. But he pointedly did not reject repeal of the tax, which many Democrats as well as Republicans have already signaled they are ready to jettison.

Republicans are also expected to mount a major attack on federal deficits.

Rep. Steve Israel of New York, in charge of the Democrats' House campaign operations, said the election returns could have been worse. They were bad enough for the president's party.

Republicans were assured of a gain of seven Senate seats, and they bid for another in Alaska, where the vote count was not complete. Also uncalled was a race in Virginia, where Democratic Sen. Mark Warner faced challenger Ed Gillespie.

Also in doubt was a Senate seat in Louisiana, where Rep. Bill Cassidy led Democratic Sen. Mary Landrieu into a Dec. 6 runoff.

Despite the reverses, Sen. Harry Reid of Nevada announced he intended to remain as the Democratic leader. There was no sign of opposition.

In the House, Republicans were within hailing distance of their largest majority since World War II, 246 seats in 1946, when Harry Truman sat in the White House.

There was no word whether Rep. Nancy Pelosi, D-Calif., would seek another term as leader.

Already, the jockeying was underway for the next election, one to pick a president in 2016.

New Jersey Gov. Chris Christie and Sen. Rand Paul of Kentucky, both Republican hopefuls, were up early for morning television appearances.