Speaker John A. Boehner of Ohio, pushing back against White House demands for no-frills legislation on the federal borrowing cap, is calling for another round of spending cuts beyond the sequester as part of any agreement to raise the debt limit.

“I believe that if we’re going to increase the debt limit, there ought to be cuts and reforms in place that are greater than the increase in the debt limit,” Boehner said in an interview Tuesday on ABC’s “Good Morning America.”

GOP aides said the speaker was affirming the “Boehner rule,” a framework he set in the last Congress that required spending cuts to match any debt limit increase. But Boehner also focused on a long-term approach to spending reductions, suggesting Republicans also will seek an overhaul of entitlement programs as part of any fiscal talks.

“A lot of these things would be phased in over a long period of time, that when you look down the road over the next 10, 20, 30 years, will have a dramatic effect on our budget deficit and our debt,” Boehner said.

In the interview, Boehner dismissed Democratic warnings that another tough round of negotiations could endanger the nation’s credit rating. He and other Republicans have supported legislation similar to a House-passed bill (HR 807) by Rep. Tom McClintock, R-Calif., that would require the Treasury Department to put a priority on the payment of principal and interest on government bonds and Social Security benefits if federal borrowing authority expires.

“Our goal here is not to default. Our goal here is to get ourselves on a sound fiscal path,” Boehner said.

The speaker provided no specific details of changes that he wanted to accompany spending cuts.

Talks in Progress

Federal borrowing authority expired on May 19, with the debt limit now set at about $16.7 trillion, but the Treasury Department has been using what it calls “extraordinary measures” to stave off the need for new borrowing authority until later this fall. A steep decline in the federal deficit in recent months along with an expected payment from government-sponsored mortgage enterprise Fannie Mae also have Treasury accounts on firmer footing this year.

But the administration still wants a deal to raise the government’s borrowing authority completed before the need for new borrowing authority is reached.

In recent days, top administration officials including Treasury Secretary Jacob J. Lew, and White House Chief of Staff Denis McDonough have held private talks with lawmakers on the debt limit.

According to several GOP tax writers, Lew made the case in a private meeting with tax writers from both parties last week for action on the debt limit close to Labor Day, saying there is still uncertainty about future revenue projections and the size of payments to the government by Fannie Mae.

Several Republicans said they were skeptical of Lew’s request for quick action on a debt limit increase for the end of the summer. “I think that we’re all for doing it. We’d just like to see some debt reduction,” said John Thune of South Dakota, chairman of the Senate Republican Conference.

Lew’s “message was we should be creating economic certainty by getting it done as soon as possible and then going on to tax reform,” said Debbie Stabenow, D-Mich., a senior tax writer.

Bob Casey, D-Pa., said the Labor Day target “was not a date certain. It was some time after Labor Day.”

A Senate GOP aide said at some point the administration will have to send a letter to Congress requesting an increase in borrowing authority, but he is unsure when that will happen.

Boehner’s proposal for “cuts and reforms” that exceed the amount of any debt limit increase drew praise from a number of Republicans. “It sounds like a promising approach,” said Senate Minority Whip John Cornyn of Texas.

But several senior Democrats lined up behind Obama’s long-standing call for a “clean” increase in the debt limit, separate from talks on the fiscal 2014 budget, a potential tax overhaul and other spending issues.

“We’re not playing with the debt limit. We’re not going to put the economy at risk over this discussion,” said Senate Budget Chairwoman Patty Murray of Washington. She and other Democrats want a budget deal that replaces automatic cuts under the sequester with a blend of alternative cuts and tax increases.

Paul M. Krawzak contributed to this report.