WASHINGTON — A new Congress opened for business Thursday to confront long- festering national problems, deficits and immigration among them, in an intensely partisan and crisis-driven era of divided government.

“The American dream is in peril,” said House Speaker John Boehner, re-elected to his post despite a mini-revolt in Republican ranks.

Moments after grasping an oversized gavel that symbolizes his authority, Boehner implored the assembly of newcomers and veterans in the 113th Congress to tackle the nation’s heavy burden of debt at long last.

“We have to be willing, truly willing, to make this right.”

Also on the agenda is the first significant effort at an overhaul of the tax code in more than a quarter century. Republicans and Democrats alike say they want to chop at a thicket of existing tax breaks and use the resulting revenue to reduce rates.

There were personal milestones aplenty as the winners of last fall’s races swore an oath of office as old as the republic.

Sens. Heidi Heitkamp of North Dakota, Elizabeth Warren of Massachusetts, Tammy Baldwin of Wisconsin, Mazie Hirono of Hawaii and Deb Fischer of Nebraska were among the newcomers sworn in, raising the number of women in the Senate to a record 20.

On the first day of a new term, one veteran made a stirring comeback. Republican Sen. Mark Kirk of Illinois returned to the Capitol for the first time since suffering a stroke a year ago, walking slowly up the 45 steps to the Capitol with the use of a cane. “Good to see you guys,” he said.

Across the Capitol, children and grandchildren squirmed through opening formalities that ended with Boehner’s election as the most powerful Republican in a government where President Barack Obama will soon be sworn in to a second term and his fellow Democrats control the Senate.

“At $16 trillion and rising, our national debt is draining free enterprise and weakening the ship of state,” said the Ohio Republican, whose struggles to control his members persisted to the final weekend of the 112th Congress when “fiscal cliff” legislation finally cleared.

“The American dream is in peril so long as its namesake is weighed down by this anchor of debt.”

Boehner will lead a House that has a Republican majority of 233-200, with two vacancies, a loss of eight seats for the GOP. Fourteen Republicans declined to vote for him, a reflection of their unhappiness with his leadership, but several more defections would have been needed to deny him a first-ballot victory.