WASHINGTON -- In the first closed-door meeting of the Republican majority in the new Congress, House Speaker John Boehner Friday promised a robust fight with President Barack Obama to cut spending in exchange for raising the nation's debt limit.

The Ohio Republican doubled down on his insistence that there must be at least a dollar-per-dollar match between spending reductions and continued borrowing.

"With the cliff behind us, the focus turns to spending," Boehner said, according to a source in the room who requested anonymity to discuss the private meeting. "The president says he isn't going to have a debate with us over the debt ceiling. He also says he's not going to cut spending along with the debt limit hike."

Treasury Secretary Timothy Geithner notified Congress earlier this week that the nation has already hit its $16-trillion debt limit, and Congress will be asked soon to raise the borrowing authority to continue paying the nation's bills. Geithner can take temporary measures to pay creditors for several weeks.

Without lifting the debt limit, the federal government would face a cataclysmic default on its already accrued obligations -- akin to stopping payments on a mortgage or credit card debt.

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Boehner and his GOP allies in the Senate, including Minority Leader Mitch McConnell (R-Ky.), are setting up a repeat of the budget wars that defined the last Congress and led to a cycle of brinkmanship and crisis.

McConnell made similar remarks in the Senate as the new Congress was sworn in.