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“Please, send us some spending cuts. This is not a fruitless exercise. You will have the support you need,” said Rep. Paul D. Ryan of Wisconsin, the committee’s ranking Republican.

But the White House says it doesn’t believe the Congress will act favorably.

Mr. Liebman said they have submitted their proposed cuts through the regular spending process, and said that’s where they’ll focus their energy over the next few months.

Even lawmakers who said they support the idea are worried about Mr. Obama’s specific proposal, saying it gives him the power to tie Congress in knots by submitting a bunch of bills all at the same time. And some are worried that it doesn’t also apply to tax cuts.

Mr. Liebman said they wanted to keep the tool focused on cutting spending, and applying it to tax cuts would be tougher because tax cuts require rewriting of laws.

Mr. Obama’s proposal is similar to one President George W. Bush announced in 2006, which passed the House on the strength of Republican votes but never got a vote in the Senate.

Mr. Spratt, current House Speaker Nancy Pelosi, California Democrat, and current House Majority Leader Steny H. Hoyer, Maryland Democrat, all voted against that proposal.