Updated: 10:38 p.m.

Senate Republicans on Monday dismissed a new budget proposal from Majority Leader Harry Reid (D-Nev.) that would exchange $2.7 trillion in spending cuts for an extension of the debt ceiling through 2013, but Democrats hope they can prove that their offering is the only viable option by week’s end.

Reid and Speaker John Boehner (R-Ohio) unveiled dueling debt ceiling proposals Monday, just more than a week ahead of the Treasury’s projected default date. Although both parties accused the other of presenting “non-starters,” no one was willing to concede that lawmakers would not make their deadline, creating a mess that’s part politics, part procedure and part posturing.

“There was a debate over whether it was just smoke and mirrors or whether it was blue smoke and mirrors. It’s not a real proposal,” Sen. John Cornyn (R-Texas) said about Reid’s plan on his way out of a Senate Republican Conference meeting Monday to review the options.

Despite mass GOP discontent with the Reid proposal — freshman Sen. Kelly Ayotte of New Hampshire called it “totally insufficient” — Senate Minority Leader Mitch McConnell (R-Ky.) refrained from offering a flat-out rejection in his remarks on the floor earlier in the day.

Reid, Boehner and McConnell had been working over the weekend on a plan, from which the Speaker’s proposal loosely draws. Although the Boehner and Reid plans differ in their timelines — House Republicans are not ready to extend the debt ceiling through the 2012 elections as President Barack Obama has asked — there are still similarities between the two offerings, such as $1.2 trillion in discretionary spending cuts over the next 10 years. It was not immediately clear, however, whether those cuts would come from the same programs and agencies.

Obama and Boehner traded blame for the stalemate in separate televised appeals to the nation Monday night. Obama accused Republicans of playing a “dangerous game” that risks a debt default in a week. But Boehner, following the president, said that Obama created the “crisis atmosphere” surrounding the debt ceiling and that it would be resolved if the Senate adopts his plan and the president signs it.

In perhaps a small signal of strategy from Senate Democrats, Reid introduced his plan on the floor Monday without formally filing cloture. Doing so likely would have brought a Senate vote Wednesday, the same day the House is set to vote on Boehner’s provision.

By waiting, Senate Democrats will see whether Boehner is able to corral enough votes from his own Conference to send his measure to the Senate. Dozens of conservative House Members have already expressed opposition to his legislation, and House Minority Leader Nancy Pelosi (D-Calif.) and Minority Whip Steny Hoyer (D-Md.) said they did not support it.

If Boehner’s solo gamble fails, Senate Democrats will have the one plan left in the procedural pipeline. If Boehner’s plan passes, they will have enough time to call it to the floor, show that it doesn’t have the votes in the Senate and hash out a compromise before the Treasury Department’s Aug. 2 deadline.

“I think it will be demonstrated clearly at the end of the week that the Boehner approach is not going to pass the Senate,” Senate Majority Whip Dick Durbin said Monday.

When asked whether either one of the bills needed to fail in order to proceed with a deal that could be sent to the president’s desk, the Illinois Democrat said: “No, we’re going to pass ours. That’s our goal.

“I continue to believe that there are Senate Republicans who are looking for an honest solution,” he said, adding he could not say the same for the House GOP.

But tea party-backed Members aren’t the only lawmakers poised to make passing a debt ceiling increase difficult. Senate conservatives can cause just as much trouble, if not more, given the rules of the chamber.

Any one Senator can hold up legislation, and staging a filibuster is “one possibility” and “something that’s come up in conversation and is being considered,” a GOP aide to a conservative Senator said. But the aide added, “Considering things are so liquid now, until there’s more hard information, I don’t think it’s fair to speak to whatever the tactics will be.”

A spokesman for McConnell would not say whether the leader was explicitly doing outreach to discourage Members from filibustering on the brink of the default deadline, only saying that the Kentucky Republican has had “several meetings with Members.”

Senators such as Jim DeMint (R-S.C.) and Rand Paul (R-Ky.) already have indicated their displeasure not just with Reid’s plan, but also with Boehner’s.

“The proposed deals being discussed today by House Republican and Senate Democrat Leaders do not make cuts to our debt. They do not solve our debt problems. They do not balance the budget, ever,” Paul said in a statement Monday. “I cannot and will not support any deal that does not have as its end goal a balanced budget. Promises and commissions will not satisfy that goal.”

House Republicans released a package that would immediately raise the debt ceiling  by $1 trillion in exchange for $1.2 trillion in cuts, even though Obama has said he would not support a plan that does not extend the limit through 2013. Senate Democrats introduced a plan with $2.7 trillion in savings, no revenues and no entitlement reform, with administration backing.

The main sticking point that tanked the weekend talks, and the Democrats’ continued point of contention with the plan Boehner released Monday, is the short-term nature of the original debt limit increase. Republicans have accused Democrats of playing politics with the timeline, while Democrats say they don’t want to repeat this struggle in six months.

“Time is running out. And with all due respect to the president, we have more important things to worry about than getting through the next election,” McConnell said.

Reid will need Senate Republicans to pass his plan, which Democrats will attach as an amendment to a pending, nonbinding Sense of the Senate resolution.

Democrats believe the plan should pass muster with Boehner, whose two major demands were that any lifting of the debt ceiling be matched dollar for dollar with cuts and that revenues not be increased. Both the Reid and Boehner plans include an outline for a joint committee to find further deficit savings in the future.

The lines of communication between the top leaders of both chambers remain open, Members and aides said Monday, and it’s possible a future compromise could be pegged to an offer that Reid made to Boehner in a meeting Saturday at the White House. The offer involved a two-step approach that would cut spending and raise the debt ceiling in the first part, then use the longer-term deficit reduction plan from the special joint committee to trigger the second part.

When asked whether he believed he would have the votes to send his plan to the House, Reid said: “I would hope so. I’m giving them what they want.”