WASHINGTON — Congressional leaders are giving tea party-backed Republican freshmen the run of the House this week with a plan to let the government borrow another $2.4 trillion — but only after big and immediate spending cuts and adoption by Congress of a constitutional amendment requiring a balanced federal budget.

This “cut, cap and balance” plan is set to pass the House on Tuesday but is sure to stall in the Senate, where majority Democrats say it would lead to decimating budget cuts and make it harder to pass tax increases on the wealthy. And even if the scheme could pass, there’s no way Congress will adopt a balanced budget amendment, which requires a two-thirds vote in both House and Senate.

But tea party lawmakers are insisting on the effort to try to put their stamp on the debate over the so-called debt limit, and GOP leaders — lacking other ideas that might win a majority in the Republican dominated House — were quick to give their OK at a spirited closed-door meeting on Friday.

Tuesday’s House vote on the cut, cap and balance plan comes after more than a week of White House talks with congressional leaders failed to produce a breakthrough. The tally will be held exactly two weeks before an Aug. 2 deadline to avoid a potentially devastating default on U.S. obligations like payments to bondholders and senior citizens receiving Social Security.

After the House exercise and a failed Senate vote on a balanced budget amendment to the Constitution, Plan B appears to be to have the Senate vote to give President Barack Obama sweeping power to order increases in the debt limit totaling $2.5 trillion over the coming year without approval by lawmakers.

The hope appears to be that after trying it their way, enough House Republicans will be able to stomach the emerging Senate plan to allow it to pass, though it’s plain there will have to be plenty of Democrats voting for it as well to make up for dozens of unyielding lawmakers unwilling to abandon their tea party promises.

For their part, Senate Republicans are demanding a vote this week on a balanced budget constitutional amendment, though they have zero chance of winning the required 67 votes.

The House Republican budget still leaves deficits in the $400 billion range after 10 years.