WASHINGTON — A new budget estimate released Wednesday shows that the spending bill negotiated between President Barack Obama and House Speaker John Boehner would produce less than 1 percent of the $38 billion in promised savings by the end of this budget year.

The Congressional Budget Office estimate shows that compared with current spending rates the spending bill due for a House vote Thursday would cut federal outlays from non-war accounts by just $352 million through Sept. 30. About $8 billion in immediate cuts to domestic programs and foreign aid are offset by nearly equal increases in defense spending.

When war funding is factored in the legislation would actually increase total federal outlays by $3.3 billion relative to current levels.

To a fair degree, the lack of immediate budget-cutting punch is because the budget year is more than half over and that cuts in new spending authority typically are slow to register on deficit tallies. And Republicans promise that when fully implemented and repeated year after year, the cuts in the measure would reduce the deficit by $315 billion over the coming decade.

Still, the analysis is an early lesson about Washington budgeting for junior lawmakers elected last year on promises to swiftly attack the deficit.

The House began preliminary debate on the measure Wednesday with it easily advancing over a procedural hurdle by a 241-179 vote. The measure appears on track to pass the House and Senate this week before a stopgap spending measure expires Friday at midnight despite opposition from some of the GOP's most ardent budget cutters.

The budget deficit is projected at $1.6 trillion this year.

The CBO study confirms that the measure trims $38 billion in new spending authority relative to current levels, but many of the cuts come in slow-spending accounts like water-and-sewer grants that don't have an immediate deficit impact.

A separate CBO analysis provided to lawmakers but not released publicly says that $5.7 billion in savings claimed by cutting bonuses to states enrolling more children and reducing the amount of money available to subsidize health care cooperatives authorized under the new health care law won't produce a dime of actual savings. CBO believes they are simply cuts to spending authority that is unlikely to be used anyway.

But those cuts to mandatory benefit programs, while producing no deficit savings, can be claimed under budget rules to pay for spending increases elsewhere in the legislation. All told, $17.8 million in such savings is claimed but just a tiny portion of it would actually reduce the deficit.

But CBO does credit a move to eliminate year-round Pell Grants with generating more than $40 billion in deficit reduction over the coming decade from both mandatory and appropriated accounts, though just slightly less than $1 billion this year.

Still, the measure halts and begins to reverse large increases for domestic agency operating budgets that have been awarded during Obama's first two years in office.

"With this bill we not only are arresting that growth but we are reducing actual discretionary spending by a record amount, nearly $40 billion in actual cuts in spending that has not ever been accomplished by this body in its history, in the history of the country," said House Appropriations Committee Chairman Harold Rogers, R-Ky. "The cuts in this bill exceed anything ever passed by the House."

Republicans say they wish the measure would cut more but that the cuts negotiated by Boehner are about as good as can be expected giver that Democrats hold the Senate and the White House. In his February budget, Obama pressed a freeze on domestic agency accounts.