A budget plan from Senate Majority Leader Harry Reid to raise the debt ceiling by $2.4 trillion, which Democrats have called “the last train out of the station” to avert default, appeared in peril Saturday — just three days out from the Treasury’s deadline.

Forty-three Senate Republicans sent a letter to the Nevada Democrat on Saturday saying they could not support his budget plan to raise the debt ceiling by Tuesday’s deadline, shortly before House Republicans planned a symbolic vote on the measure. Reid and Minority Leader Mitch McConnell engaged in a lengthy political sparring match on the Senate floor, arguing about everything from the nature of negotiations that died last week to the definition of a filibuster.

Most striking about the exchange, however, was McConnell’s adamancy that Reid’s plan was going nowhere, even after it had been amended Friday to include a mechanism devised earlier this month by the Kentucky Republican himself that would raise the debt ceiling in a series of three votes and shift the political burden of doing so to Democrats.

“I want to disabuse my friend of the notion that somehow [his plan] is going to pass,” McConnell said to Reid on the floor. “The measure … is not acceptable to the Senate, is not acceptable to the House, will not pass.

“Let’s get to talking to the administration again in the hopes that we can get together behind something that can pass both the Senate and the House and be signed into law before Tuesday,” McConnell continued.

Talks with President Barack Obama broke down last week after Speaker John Boehner (R-Ohio) backed away from a tenuous, $3 trillion “grand bargain” two Fridays ago and the four top Congressional leaders huddled at the White House on Saturday, with the president tasking the lawmakers with the responsibility of coming together and finding any plan that might be able to clear Congress.

So far, that haul has been heavier than expected. Boehner needed an extra 24 hours to approve his own budget offering, actively and painfully whipping each and every last vote to send his bill to the Senate. Meanwhile, leaders in the Senate were put in a holding pattern as the House votes stalled, shortening the clock for Senators already bound by time-consuming rules that could push final passage votes on any plan to Monday at the earliest, but more likely Tuesday, if then.

The letter from the 43 Republicans — not signed by GOP Sens. Lisa Murkowski (Alaska), Scott Brown (Mass.), Olympia Snowe (Maine) and Susan Collins (Maine) — expressed the opposition of the majority of the Conference to Reid’s offering, a position they believed would be bolstered by the House votes.

“Given the nation’s enormous future spending challenges, it would be irresponsible to give the President this unprecedented additional borrowing authority without requiring the enactment of significant spending reductions and reforms,” the letter reads. “We urge you to abandon this reckless proposal and instead pursue a more responsible course of action that would rein in spending, reassure the financial markets, and help promote private sector job growth.

The letter was dated Friday, however, and McConnell’s office would not say definitively whether Members had signed the letter before or after Reid’s changes to the legislation, which include the Republican leader’s framework that boosts the president’s authority to raise the debt limit by constructing the extension of the nation’s borrowing capacity as a series of votes of “disapproval.”

“Our Members signed a letter to oppose the Reid plan, and that applies to the Reid plan as it stands today,” McConnell spokesman John Ashbrook said.

Reid indicated Saturday that he has been speaking with a few rank-and-file Republicans about how to amend his offering to make it more palatable. To clear the first procedural vote on his plan, slated for 1 a.m. Sunday, Reid needs 60 votes. Fifty-three Members caucus with the Democrats, though Sen. Joe Manchin (D-W.Va.) expressed his reservations about Reid’s offering earlier this week and the four Republicans who did not sign McConnell’s letter will not be enough to tip the scales.

“I would have hoped, though, that someone would come to us, come to the table, the bargaining table on behalf of the Republican caucus with ideas to improve a proposal already cut from Republican cloth,” Reid said on the floor Saturday. “Democrats are willing to sit down and negotiate. My door is still open.”

Sources close to both Reid and McConnell, however, said that the lines of communication between the two leaders — usually very open — recently have closed off.