House Speaker John Boehner told members of his GOP conference Friday that he plans to use the upcoming battle over raising the federal debt ceiling as leverage for more spending cuts.

Speaking at a closed-door meeting of House Republicans, Boehner said it was time to focus on spending now that the fiscal cliff has been temporarily averted.

"With the cliff behind us, the focus turns to spending," Boehner said, according to a source in the room. "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."

Right after the House passed the fiscal cliff compromise, President Barack Obama said, "I will not have another debate with this Congress over whether or not they should pay the bills that they've already racked up through the laws that they passed."

If the ceiling isn't raised by late February or early March, the United States runs the risk of defaulting on its obligations because the Treasury would no longer have enough money available to pay all the country's bills.

In the meeting, Boehner cited survey figures from a GOP-sponsored pollster showing a majority of Americans agreeing that increasing the debt limit must be paired with spending cuts.

"That's the principle I laid out before the Economic Club of New York in May of 2011, and I've repeated a number of times since. The debate is already underway," Boehner said, according to the source.

Spending cuts were not included in the final deal avoiding the fiscal cliff, despite a last-minute effort by Boehner to amend them into the bill. Some conservatives blamed Boehner for his handling of the fiscal cliff solution, and on Thursday he weathered some resistance in his re-election to the speaker post.

The speaker confirmed to CNN before the speakership vote that he's told his GOP colleagues he's going to back off attempting one-on-one negotiations with President Barack Obama to pre-cook major deals, after the two men failed to reach an agreement averting the fiscal cliff. The deal that eventually passed was brokered by Vice President Joe Biden and Sen. Mitch McConnell, the Republican leader in the Senate.

"Regular order works best," Boehner said -- meaning he'll follow normal legislative process in the future by introducing bills in the House that would eventually be sent to the president.

Boehner added that he's "always happy to talk to the president."