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In the latest gambit out of Washington's head-spinning budget debate, House Majority Leader Eric Cantor announced Wednesday that if the Senate fails to act by next week, Republicans will proffer a bill forcing an earlier House GOP plan that did not pass Congress to become the "law of the land."

The proposal outlined Wednesday would be an unusual and likely unconstitutional move. Under the bill, the $61 billion budget that passed the House last month and subsequently went nowhere would go into effect if the Senate does not approve a budget by April 6. Plus, it would provide that in the event of a shutdown lasting more than 24 hours, members of Congress and President Obama wouldn't get paid retroactively for the days the government was shuttered.

The proposal is meant to put pressure on the Senate to give Congress some kind of spending plan to work with so that the government does not arrive empty-handed on its April 8 deadline without a budget, forcing lights out.

But the proposal raises all manner of constitutional and practical questions.

First, it would effectively deem a prior bill passed, even though it did not clear the Senate or win the president's signature. Second, it's unclear why or whether Republicans think the Senate and president would accept the so-called "Government Shutdown Prevention Act" when they didn't approve the initial House plan.

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Cantor spokeswoman Laena Fallon said that's a question for Senate Democrats.

"But it is our hope," she said, "that this bill will, at a minimum, spur the Senate to pass some bill funding the government for the rest of the year."

Following the announcement, Senate Democratic Caucus spokesman Brian Fallon reiterated that the old GOP-backed budget was "going nowhere," calling the latest proposal a "show vote being staged so that Congressman Cantor can throw a bouquet to the Tea Partiers."

The proposal seemed to be pitched as a Plan B while fragile budget negotiations resumed Wednesday on Capitol Hill. After several days marked by fingerpointing and stalemate, a senior congressional official close to the talks said House Speaker John Boehner's staff met with aides to Senate Democratic Leader Harry Reid Tuesday night in Reid's office.

"While our office negotiates with Speaker Boehner's office, the Republicans who aren't in the room should work with Democrats to pass bills that create jobs and help struggling families instead of wasting time on symbolic stunts and continuing to cling to a bill that has already been rejected by the Senate and would kill 700,000 American jobs," Reid spokesman Jon Summers said in a statement.

During a press conference Wednesday morning, a fired-up Boehner pressed the Senate to make the next move.

"Now the Senate says we have a plan. Well, great. Pass the damn thing, all right!" Boehner said. "And send it over here, and let's have real negotiations."

Reid said he's glad Boehner "returned to the conversation," and urged him to resist the "radical" wing of his party.

The size of the package being talked about in the Senate may end up splitting the difference between the two parties' earlier proposals. Republicans for weeks have pushed a plan to cut $61 billion from last year's spending levels, but senior GOP Senate aides indicated the caucus could settle for a Democratic counterproposal that would achieve half that.

As talks inch forward, the two parties are not just trying to find elusive middle ground on budget cuts. They're now trying -- or at least some are -- to work against a backdrop of increasingly hostile talking points.

Democrats have put out the message that "extreme" Tea Party-aligned lawmakers are preventing Republican leaders from making any headway. Though Tea Party groups indeed clamor for significant spending cuts, GOP leaders called it ridiculous to blame the Tea Party for the stalemate.

Republicans were emboldened after Sen. Charles Schumer, D-N.Y., was heard before the start of a conference call telling other Democrats that they should use the word "extreme" to describe Republican demands, because "that's what the caucus instructed me to do the other week."

Cantor, R-Va., seized on Schumer's hot-mic moment.

"Chuck Schumer did us a favor. He exposed their tactic. He's telling his members to deem any spending cut as unreasonable. I don't see how we can do anything if they're not set serious." Cantor said.

Republicans have shown no qualms about throwing Schumer's choice adjective back at the Democrats.

"What Chuck Schumer and the Democrats are doing to this country is extreme," said Sen. Rand Paul, R-Ky., a Tea Party-aligned freshman lawmaker, referring to the U.S. government's voracious borrowing.

Each party preemptively is arguing that the other is to blame for a government shutdown, should negotiations fail completely. Each also argues that budget talks would be going more smoothly if only the other party didn't control half of Congress.

Those arguments, though, do little to bring lawmakers together on a budget number that can pass Congress and win the president's signature. And time is running short -- not only does Congress need to figure out a short- or medium-term budget by April 8 or face shutdown, but lack of progress on this budget imperils another more critical vote on whether to raise the debt ceiling.

Frustrated lawmakers have threatened to blow up that vote, a scenario administration officials say could cause the United States to default on its debt.

Sen. Marco Rubio, R-Fla., wrote in a column Wednesday that he will vote against an increase "unless it is the last one we ever authorize" and tied to several tax-and-spending reforms, including to entitlements.

"The president and others want to raise this limit. They say it is the mature, responsible thing to do. In fact, it's nothing more than putting off the tough decisions until after the next election. We cannot afford to continue waiting. This may be our last chance to force Washington to tackle the central economic issue of our time," Rubio wrote.

Republicans are determined to seek deep cuts in spending in future budgets, regardless of the debate over the 2011 budget. One senior Senate GOP aide said Republicans should, at this point, accept Democrats' latest proposal for this year's spending and then resolve to cut more in the fiscal 2012 proposal.

The Democrats' proposal is said to include between $20 billion and $25 billion in cuts for the rest of 2011 -- on top of the $10 billion that has been cut over the course of two stopgap bills.

Fox News' Trish Turner and Chad Pergram contributed to this report.