The 113th US Congress, featuring dozens of new faces in the House and Senate, convened Thursday fresh from the year-end "fiscal cliff" fiasco, as lawmakers cast a wary eye towards the tough budget battles ahead.

Twelve freshman senators and 82 newly-elected congressmen took the oath of office, with President Barack Obama's Democrats enjoying modest gains in both chambers.

But the balance of power remains divided on Capitol Hill: Democrats control the Senate, while Republicans hold sway in the House of Representatives, where John Boehner kept his job as speaker.

There was little expectation that he would lose the leadership role, but Republican infighting over backing a fiscal cliff deal that hikes taxes on the wealthy triggered speculation about Boehner's hold on the gavel.

Lawmakers burned the midnight oil in the waning days of the 112th Congress hammering out a deal to prevent $500 billion in tax increases and spending cuts from kicking in on January 1 -- and possibly tipping the US economy back into recession.

But larger budget battles are on the horizon, particularly over US borrowing, an extension of the government's 2013 budget, and the now-looming spending reductions set to hit the Pentagon as well as most domestic programs.

The Senate's Republican Minority Leader Mitch McConnell welcomed the new members, and offered warm words to Senator Mark Kirk, who returned Thursday after spending most of 2012 recovering from a stroke.

But McConnell quickly turned to what he called "the transcendent challenge of our time."

The out-of-control federal debt, McConnell said, is "so huge it threatens to permanently alter (our) economy," he told the Senate.

McConnell acknowledged his last-gasp deal forged with Vice President Joe Biden was an "imperfect" one that went against Republican no-new-taxes orthodoxy.

But with the battle over taxes behind them -- the deal raises rates for individuals earning over $400,000 and on couples earning more than $450,000 -- McConnell was already eyeing the looming bout over spending and the debt ceiling.

"It's time to face up to the fact that our nation is in grave fiscal danger, and that it has everything to do with spending," he said, throwing down the gauntlet to Obama.

"The president knows as well as I do what needs to be done. He can either engage now to significantly cut government spending or force a crisis later," McConnell added. "It's his call."

Obama left Washington to resume his Hawaii vacation hours after the "fiscal cliff" deal was approved by Congress late on New Year's Day, and signed the legislation Wednesday by auto-pen.

But Biden was on hand to swear in the new senators, including five women, bringing to a record 20 the number of female senators, as well as Tim Scott, the first black Republican in the Senate since 1979.

"Enjoy it," Biden told the newcomers, adding that he missed the chamber where he served for 36 years.

"The best time I ever had in my life was serving here," he told AFP off the Senate floor.

Asked about the trio of looming fiscal fights, Biden expressed confidence that the White House and lawmakers would overcome their differences.

"We've always had the battles, and we get through," he said.

The Biden-McConnell deal largely averted a financial crunch that had global repercussions, but the International Monetary Fund, rating agencies and analysts have warned that the critical problem of deficits and debt still hang over the US economy.

Financial markets cooled Thursday over the last-minute agreement, in contrast to the initial stocks surge which had greeted the deal Wednesday.

The hard-fought agreement, seen as a political victory for Obama, raised taxes on the very rich and delayed the threat of $109 billion in automatic spending cuts for two months.

The respite will prove temporary: aside from clashes on spending cuts, there are worries over lifting the debt ceiling -- also at the end of February.

Analysts say the country could see a repeat of the 2011 row that saw Washington's credit rating downgraded for the first time.

Nancy Pelosi, re-elected to her role as House Democratic leader, took a conciliatory tone.

"I hope with all my heart that we find common ground," she told the chamber.

Boehner called for a fresh start after the startlingly unproductive record of the 112th Congress, reminding lawmakers to resist the pull of special interests and "follow the fixed star of a more perfect union."

But he turned swiftly to the "peril" of America's $16 trillion debt, saying it is "draining free enterprise and weakening the ship of state."