Obama, in a statement wishing Republicans well, said there will be "pitched battles" with Congress but that there are also "enormous areas of potential agreement."
Last year's Congress, which was badly gridlocked, has been dubbed one of the least productive in history.
Boehner's detractors in Tuesday's vote were conservative activists, some of them junior members, who regularly have voted against House Republican leadership-backed bills. But they also included seven-term Representative Steve King of Iowa, who has helped stymie Boehner's efforts to advance major changes to US immigration laws.
VETO THREAT
Meanwhile, Idaho's Raul Labrador, who declined to vote for Boehner in the Speaker's election two years ago, supported him on Tuesday, as did Tea Party darling John Fleming of Louisiana.
"As Speaker all I ask and frankly expect is that we disagree without being disagreeable," a tearful Boehner told House members after the election. Boehner is often overcome by emotion at the start of a new Congress.
In coming weeks, Boehner is expected to face the difficult task of finding a middle ground on a bill to keep the Department of Homeland Security operating beyond February when funds run out.
House conservatives want to use that bill to withhold federal funds for the department's employees to implement Obama's order easing the threat of deportation for millions of undocumented residents.
Such a move would likely draw a veto from Obama, threatening operations of one of the most important federal agencies in the post-Sept. 11, 2011 era.
Republican Senator Mitch McConnell, who assumed the Senate majority leader job on Tuesday and has been hoping to avoid any government shutdown fights this year, could temper such House legislation and force Boehner's Republicans to compromise.
McConnell has influence over the House because the Senate will need to approve any legislation for it to win final passage.