House Speaker John Boehner only narrowly won a second term as the chamber's leader Thursday, the opening day of the 113th Congress, a signal that Boehner's fellow Republicans are still upset with his handling of negotiations with the White House over tax increases and spending cuts.

Boehner won a second term by just seven votes, one of then narrowest margins of any speaker, just two days after clashing with conservatives over a bill, passed New Year's Day, that averted the so-called fiscal cliff but raised taxes for some Americans and included none of the cuts in federal spending conservatives were demanding.

The speaker took the gavel with a nod to his disgruntled members, promising his priority in this new Congress would be to reduce the nation's rising $16.4 trillion in debt.

"The American Dream is in peril so long as its namesake is weighed down by this anchor of debt," Boehner told the chamber. "Break its hold, and we begin to set our economy free. Jobs will come home. Confidence will come back."

Congress and the White House will almost immediately begin debate over whether to increase the debt ceiling, the limit on how much the federal government can borrow. The government will hit the $16.4 trillion limit in a matter of weeks and might have to default unless Congress allows it to borrow more. Republicans vowed not to raise the limit unless the increase is matched by further spending cuts.

A number of House Republicans say they have doubts about Boehner's ability to win additional cuts after he failed to prevent Obama from raising taxes on the wealthy.

Ten Republicans voted against Boehner on Thursday, casting ballots for current and former members, including outgoing Rep. Allen West, of Florida, and Majority Leader Eric Cantor, of Virginia. Two others abstained during the vote, and a third skipped the vote.

Rep. Walter Jones, R-N.C., one of those who voted against Boehner, said opposition to the speaker had actually dwindled by the time the vote was taken. A day earlier, fresh off the vote on the tax increase, there were enough votes against Boehner to deny him a second term, he said. But that opposition faded because some members feared retribution from the Republican leadership.

Boehner yanked Jones and three other Republicans from coveted committee assignments last month because they bucked the leadership, and other potential defectors feared the same treatment.

Jones said conservatives hoped to force a second vote for speaker Thursday to signal their frustration with Boehner.

"If we had been able to go to a second round, that would have been one hell of a statement," Jones told The Washington Examiner. "The statement, quite frankly, is that we need to go back to conservative principles."

Rep. Tom Cole, R-Okla., a longtime ally of the leadership who was sworn in for a fifth term Thursday, said Boehner will stand firm on spending cuts in upcoming negotiations with Obama.

"Think of this as a four-course meal," Cole said. "The president got to eat his dessert first, and next is spinach, carrots and peas. He's already gotten his revenue, and this is going to be about spending cuts and entitlement reform. If the president thinks this is going to be about any additional revenue, he's just wrong."