WASHINGTON (AP) — The White House is counting on Republican lawmakers to support new tax revenues as part of an overarching plan to reduce long-term deficit and pave the way to increase the government’s borrowing authority.

White spokesman Jay Carney said Wednesday that President Barack Obama’s is confident that there are enough lawmakers from both parties to support a deal that would reduce the debt by as more than $2 trillion over the next 10 years with spending cuts and tax increases.

Republican leaders have been adamant in public statements that they will oppose any tax hikes.

“The president believes, we believe, that there are enough members of both parties in both houses who support the idea that a big deal has to be balanced and therefore include spending cuts in the tax code,” Carney said, employing a phrase White House officials use to describe ending tax loopholes and tax subsidies for certain taxpayers and corporations.

The assertion reinforced and expanded on Obama’s comments Tuesday that back-channel talks with congressional leaders last weekend produced new progress in advance of a White House session Thursday on deficit reduction. While suggesting progress, Carney said no final deal should be expected from Thursday’s meeting.

The president is siding with House Speaker John Boehner in insisting that negotiators resist the temptation to “kick the can down the road” and settle for a makeshift, short-term solution to stave off a first-ever U.S. default next month.

At issue is the need to raise the government’s so-called debt limit to avoid a default on its obligations to bondholders and Social Security beneficiaries. Republicans want deficit cuts in the range of at least $2.4 trillion over 10 years to offset the amount of new government borrowing needed simply to avoid another vote before 2013.

Obama met with Boehner on Sunday, the first session since Republicans last month abandoned negotiations being led by Vice President Joe Biden. Carney On Wednesday declined to discuss that meeting, refusing even to acknowledge that it had occurred. He said the negotiations had a better chance of success if the details of the talks were kept under wraps.

The Biden talks had produced a series of tentative understandings on potential spending cuts totaling at least $1.6 trillion under administration math and $2 trillion or more under GOP math. But negotiators say a true agreement on those cuts — to day-to-day agency operating budgets, defense, federal pensions and farm subsidies, among other things — would require further sacrifice in the political priorities of Democrats and Republicans alike.

A Republican budget plan passed by the House earlier this year aimed to reduce the deficit by more than $5 trillion over 10 years. Obama also unveiled the broad outlines of a plan that would reduce the deficit by $4 trillion over 12 years. Carney said the $4 trillion mark remained “something to aspire to,” even though talks have focused on reaching about half that amount.

The administration says that if the government’s borrowing authority is not increased by Aug. 2, the U.S. will face its first default ever, potentially throwing financial markets into turmoil.

Obama isn’t calling for increases in tax rates. On Tuesday, the president urged Republicans to agree to eliminate “certain tax breaks and deductions for the wealthiest of Americans.” The White House is pressing for the repeal of tax breaks enjoyed by the oil and natural gas industry and limits on deductions claimed by people in the 35 percent tax bracket.

On Tuesday, Boehner attacked the latter proposal as an assault on small businesses but was subdued on questions like oil and gas subsidies or a much-publicized tax provision that gives favorable treatment to companies that buy corporate jets.

“We’re not dealing just with talking points about corporate jets or other ‘loopholes,'” Boehner, R-Ohio, said. “The legislation the president has asked for, which would increase taxes on small businesses and destroy more American jobs, cannot pass the House, as I have stated repeatedly.”

In his remarks Tuesday, Obama said he strongly opposes a stopgap, short-term debt-limit increase, as suggested by some lawmakers.

“We’ve made progress, and I believe that greater progress is within sight, but I don’t want to fool anybody. We still have to work through some real differences,” the president said.

Obama’s tone was less partisan than at a news conference last week, as were the responses from Capitol Hill Republicans.

“I’m pleased the president stated today that we need to address the big, long-term challenges facing our country,” Boehner said in a statement.