Boehner voiced doubts about Obama's proposal for taxpayer-funded help for preschool education for all 4-year-olds, and would not commit to passing a pathway to citizenship for the nation's 11 million illegal immigrants, though doing so would be "somewhat helpful" to members of his party.
"There's no magic potion that's going to solve our party's woes with Hispanics," he said.
He also refused to endorse any of Obama's gun-control proposals and said he opposed a plan to raise the minimum wage to $9 an hour.
The Ohio Republican said he gets along well with Obama but admits their relationship hasn't generated much in the way of results, pointing to two failed rounds of budget talks in 2011 and at the end of last year. Boehner said he was frustrated that spending cuts Obama signaled he would agree to in 2011 had been taken off the table since the election.
"Every time I've gotten into one of these high-profile negotiations, it's my rear end that got burnt," Boehner said. "It's just probably not the best way for our government to operate."
The immediate future, though, is dominated by $85 billion in automatic, across-the-board spending cuts - called a sequester in Washingtonspeak - set to slam the Pentagon and domestic programs over the coming seven months. Boehner said he had no plans to resurrect legislation passed by Republicans last year to block this year's sequester.
The speaker said that until Obama puts forward a plan to avoid the sequester and Senate Democrats pass it, "we're going to be stuck with it. It's going to be a little bleak around here when this actually happens and people actually have to make decisions."
Boehner noted that while plenty of GOP defense hawks were anxious about the automatic cuts, Democrats concerned with cuts to domestic programs have a lot on the line, too.
He sounded glum about prospects that the two sides would come together in the spring on a separate, long-term budget blueprint to address the government's fiscal problems.
"It's hard to imagine that you could reconcile [the separate budgets] the House and Senate pass," he said. "But at some point, in some manner, it almost has to happen if we're going to deal with our long-term spending problem."
In March, the House and Senate will take up competing long-term budget blueprints. In a break with past years, House Republicans promise to balance the budget within a decade - without additional tax increases beyond the $600 billion-plus in tax increases on wealthier earners won by Obama as part of a deal to keep the rest of the Bush-era tax cuts.
Boehner said that an impasse with Senate Democrats, who insist their rival budget plan will raise taxes and contain softer budget cuts, is probably inevitable.
Also looming is the need to pass legislation financing the government through the budget year ending Sept. 30. Here, at least, Boehner saw some promise, predicting a resolution will pass soon to head off a partial shutdown.
Washington's most powerful Republican was also noncommittal on two of Obama's top second-term initiatives: overhauling the nation's immigration laws and enacting stricter gun-control measures.
On immigration, Boehner said he was "encouraged" by bipartisan efforts to overhaul the nation's fractured laws, but he would not say whether he would support a bill that includes a pathway to citizenship for 11 million illegal immigrants. Nor would he commit to a pathway to citizenship for the so-called dreamers - young people brought to this 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 said he would consider measures passed by the Senate but would not pledge to hold votes on any of Obama's core principles, including universal background checks for all gun purchasers. The expanded checks are broadly supported by the public.
While not outright opposing background checks or Obama's other calls for limiting assault weapons and high-capacity ammunition magazines, the speaker said he preferred focusing on the link between mass shootings and mental-health issues.
"When you look at all these mass shootings, almost every one of the individuals involved has a history of mental illness," Boehner said.