"We hope he is willing to work with us on these priorities. But as I have said, our new majority will be the voice of the American people as they expressed it so clearly yesterday," Boehner said.
Boehner was joined at a news conference by Senate Republican Leader Mitch McConnell of Kentucky and Mississippi Gov. Haley Barbour, who headed the GOP campaign organization that helped gain 10 governorships.
McConnell was more pointed than Boehner, saying that what Democrats who were defeated at the polls "learned is that choosing the president over your constituents clearly doesn't work."
Republicans will "work with the administration when they agree with the people and confront them when they don't," McConnell said.
He said he hoped Obama would work with Republicans "on things like spending and debt and trade agreements and clean coal technology and nuclear power. ... The question is how do we meet in the middle."
A leader of a stronger minority in the Senate - but a minority nonetheless - McConnell said, "While clearly the election did not transfer full control of the government to the opposition, it is the first step in changing the direction of what we have been doing in Washington."
The takeover of the House followed a four-year turn in the minority for Republicans, who have stressed publicly that they view their triumph as a second chance given by voters who stripped them of power in 2006.
In a news conference lasting only about 15 minutes, Boehner said at least a half-dozen times that Republicans would "listen to the voice of the American people" as they draft legislation to steady the economy, cut spending and reduce the scope of the federal government.
Boehner said Speaker Nancy Pelosi had tried to reach him by phone. "She left me a very nice voicemail," he said, adding he felt confident there would be a smooth transition as Republicans take over the reins of power in the House.
He also said he didn't see any difficulty incorporating new GOP House members supported by the tea party into the chamber's Republican team. Many of them campaigned on the basis of deep spending cuts or other proposals that could prove intensely controversial, including steps to privatize Social Security or eliminate entire agencies of government.
The new Congress convenes in January, and Boehner said Republicans would use the interim to decide precisely how to proceed with an agenda aimed at helping an economy still struggling to emerge fully from the worst recession since the 1930s.
Lawmakers return to the Capitol in two weeks for a post-election session to wrap up loose ends from the past two years, and a vote is expected on extension of tax cuts passed during the Bush administration that are due to expire on Jan 1.
Obama and fellow Democrats have said they want to extend cuts for individuals at incomes under $250,000, while Republicans want cuts kept in place for all income levels.