Washington ? House Republican budget negotiators have abandoned plans to pursue a massive $4 trillion, 10-year deficit reduction package in the face of stiff GOP opposition to any plan that would increase taxes as part of the deal.

House Speaker John Boehner informed President Barack Obama Saturday that a smaller agreement of about $2 trillion was more realistic.

In a statement issued Saturday evening, Boehner said: “Despite good-faith efforts to find common ground, the White House will not pursue a bigger debt reduction agreement without tax hikes.”

The White House responded that Obama will continue to push to make as much progress on deficit reduction as possible.

Boehner’s statement came a day before he and seven of the top House and Senate leaders were scheduled to meet at the White House in a negotiating session and lay out their remaining differences.

A deficit reduction deal is crucial to win Republican support for an increase in the nation’s debt ceiling. The government’s borrowing capacity is currently capped at $14.3 trillion and administration officials say it will go into default without action by Aug. 2.

Obama tried to build political support for an ambitious package of spending cuts and new tax revenue that would reduce the debt by $4 trillion over 10 years. But from the moment he proposed it, Republicans said they would reject any tax increases and Democrats objected to spending cuts in some of their most prized benefit programs, including Medicare, Medicaid and Social Security.

A bipartisan group of lawmakers led by Vice President Joe Biden had already identified, but not signed off on, about $2 trillion in deficit reductions, most accomplished through spending cuts.

But after holding a secret meeting with Boehner last weekend, Obama and his top aides said they believed an even bigger figure was attainable if both parties made politically painful, but potentially historic, choices.

In the end, the pressure from both sides was pushing against Obama’s bigger goal.

“I believe the best approach may be to focus on producing a smaller measure, based on the cuts identified in the Biden-led negotiations, that still meets our call for spending reforms and cuts greater than the amount of any debt limit increase,” Boehner said.

White House Communications Director Dan Pfeiffer said that Obama intended to continue to push for as big a deficit reduction number as possible and that tax revenue be part of the mix.

“The president believes that solving our fiscal problems is an economic imperative. But in order to do that, we cannot ask the middle-class and seniors to bear all the burden of higher costs and budget cuts,” Pfeiffer said. “We need a balanced approach that asks the very wealthiest and special interests to pay their fair share as well, and we believe the American people agree.”