But it's the economy and deficit at the top of the congressional priority list as Obama and lawmakers face looming fiscal crises confronting the nation: the deep automatic spending cuts, called a "sequester," to take effect March 1, followed by the government running out of money to fund federal agencies March 27.
Boehner, seeking to keep the government from lurching from one crisis to another, has also pressed for Washington to get back to passing regular budgets. But he expressed pessimism about whether that was possible given the deep divisions on Capitol Hill.
"It's hard to imagine that you could reconcile what the House and Senate pass, but at some point, in some manner, it almost has to happen if we're going to deal with our long-term spending problem," Boehner said.
The Ohio Republican also reiterated his opposition to letting the sequester take effect, and served up a reality check to members of his caucus who say publicly that they would be willing to let the $85 billion in across-the-board cuts take effect on March 1.
"None of them have ever lived under a sequester. For that matter, neither have I," Boehner said. "This is going to be a little bleak around here when this actually happens and people actually have to make decisions."
The president wants to put off the sequester through a combination of targets spending cuts and increased tax revenue. Republicans want to offset the sequester with spending cuts alone.
Obama also used the prime-time speech Tuesday to call for action on a broad agenda that included the economy, guns, immigration, taxes and climate change. He offered new initiatives on voting, manufacturing, and research and development. He said he wanted to raise the minimum wage, lower energy use, and expand pre-school programs for all 4-year-olds.
While Obama left out key details of the pre-school program, including the cost to the federal government, administration officials said ahead of Tuesday's speech that the proposal would include the government providing financial incentives to assist states. The president is expected to campaign on the proposal Thursday in Georgia.
Boehner questioned the need for the federal government to get involved in early childhood education, saying it was "a good way to screw it up."
During a visit Wednesday to Asheville, N.C., Obama promoted his ideas on creating jobs and closing the income gap between the wealthiest and middle-income Americans. The president used a retrofitted former Volvo plant to make a case for proposals designed to encourage companies that have operated overseas to bring back jobs to the U.S.
"We're seeing this trend of what we call insourcing, not just outsourcing," Obama said. "And the reason is because America has got outstanding workers. We're starting to produce more homegrown energy, which is driving down our energy costs. And, obviously, we've still got the biggest market in the world. And if we try to improve our infrastructure a little bit more, then we're going to be even that much more competitive."
The president also used his State of the Union address to call on Congress to pass comprehensive immigration legislation with a pathway to citizenship for 11 million illegal immigrants and hold votes on a series of gun-control measures introduced following the shootings of 20 school children in Newtown, Conn.
Boehner has been noncommittal on his position on key components of both proposals.
On immigration, Boehner told the AP that he was "encouraged" by bipartisan congressional efforts to address immigration reform. But he refused to take a position on providing a pathway to citizenship for illegal immigrants, including for young people who were brought to the country illegally.
"I'm not getting myself locked into a corner on what I'm for or what I'm against," he said.
On gun control, Boehner wouldn't commit to holding votes on universal background checks or bans on assault weapons and high-capacity ammunition magazines. Instead, he focused on exploring the link between mass shootings and mental health.
"What I don't want to be is parceled into some political stunt that has no impact on the problem," Boehner said.