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The administration minces no words in making clear how serious it sees this test. Mr. Obama has indicated that he would veto a defense policy bill that includes the extra engine, even if that bill includes his long-sought reversal of the “don’t ask, don’t tell” policy on gays serving in the military.

Geoff Morrell, press secretary at the Pentagon and spokesman for Defense Secretary Robert M. Gates, said last year they left Congress wiggle room and lawmakers added $465 million in funding for the second engine. This year, that’s changed.

“This is make-or-break as far as he is concerned. He will go to the mat in order to ensure there is no more funding for a program that we see no more utility in,” Mr. Morrell said. “We have been forced, despite our protestations, to eat roughly half a billion dollars a year in funding for the extra engine for the last few years, and we simply can no longer afford to do that.”

Spending has emerged as a major issue over the past few years, but has risen to new levels as the economy turned sour under the presidencies of George W. Bush and Mr. Obama.

The call for cuts has grown particularly loud in recent weeks. Over the weekend, House Majority Leader Steny H. Hoyer, Maryland Democrat, suggested that he would be willing to dip into the stimulus funds to pay for some new programs.

Republicans say they’ve learned the lessons of overspending during Mr. Bush’s tenure and want to pressure Mr. Obama to join them in cutting the budget.

Mr. Cantor and House Majority Leader John A. Boehner, Ohio Republican, sent letters to Mr. Obama twice this year begging him to submit his list of 53 cuts and 30 reductions to Congress under budget rules for rescissions.

Mr. Boehner and Mr. Cantor said they would work to round up the one-fifth of members it would take under current budget rules to force House floor votes on the cuts and reductions.

Previous presidents made use of rescission authority. President Clinton won $3.6 billion in savings from 111 cuts, President George H.W. Bush won $2.4 billion from 34 cuts and President Reagan got Congress to cut 214 programs for $15.7 billion in savings.

But President George W. Bush never made use of the authority, and Mr. Obama has not done so either.

Last week, Peter Orszag, Mr. Obama’s budget director, said the administration doesn’t think the Democrat-controlled Congress would take cuts seriously.

“It just comes down to a question of whether it’s a fruitless exercise because you have a very low probability of success in the current environment,” Mr. Orszag said. “We would rather put our effort, which we are doing, into the structural change of getting that authority, rather than sending up a package under the existing authority, which is much more limited, that would go nowhere.”

Mr. Obama, like Mr. Bush before him, has called for Congress to adopt new rules that would force Congress to act on spending-cut proposals. But that proposal has attracted just 20 co-sponsors in the House, eight in the Senate, and has earned opposition from some key lawmakers.

That leaves congressional Republicans, congressional Democrats and Mr. Obama in a three-way standoff - the legislative version of the showdown between Clint Eastwood and two other gunslingers at the end of “The Good, the Bad and the Ugly.”

Each side is looking for another to blink, with the result that spending cuts are proving tough to secure.

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