WASHINGTON (AP) — Senate Democratic leader Harry Reid served notice Friday that he's pushing ahead with his debt-limit bill as House Speaker John Boehner's rival measure languished in limbo, further escalating a wrenching political standoff that has heightened fears of a market-rattling government default.

"This is likely our last chance to save this nation from default," Reid declared glumly on the Senate floor, as a Tuesday's deadline drew closer.

Reid's move came with Boehner's bill still in wait of a vote and a bitter standoff between GOP leaders and their conservative rank and file. Demoralized House Republicans were striving for a third straight day to pass the Boehner bill, even though it had virtually no chance of surviving the Senate.

Reid, D-Nev., said he had invited Senate Minority Leader Mitch McConnell, R-Ky., to join him in negotiations.

"I know the Senate compromise bill Democrats have offered is not perfect in Republican' eyes. Nor is it perfect for Democrats," Reid said. "But together, we must make it work for all of us. It is the only option."

Reid's move sets up a showdown vote on Sunday.

McConnell dismissed the Democratic effort, arguing that it stands no chance in the GOP-controlled House and blamed Obama for pushing the nation to the brink of an economic abyss.

"If the president hadn't decided to blow up the bipartisan solution that members of Congress worked so hard to produce last weekend, we'd be voting to end this crisis today," McConnell said on the Senate floor.

Underscoring the mad scramble in Congress for an elusive solution, both chambers recessed moments after opening speeches.

Boehner, R-Ohio, suffered a stinging setback Thursday when, for a second consecutive day, he had to postpone a vote on his proposal to extend the nation's borrowing authority while cutting federal spending by nearly $1 trillion.

"Obviously, we didn't have the votes," Rep. David Dreier, R-Calif., said after Boehner and the GOP leadership had spent hours trying to corral the support of rebellious conservatives.

Republicans were trying again Friday. If they continued to fail, then President Barack Obama and Senate Democrats would have extensive leverage to shape a bill to their liking and practically dare the House to reject it and send the nation into default.

If, however, Republicans can get Boehner's version through the House, a rapid and complex set of choices will determine whether and how a debt crisis can be averted. House Republicans will be under tremendous pressure to pass something, even if they have to make it so appealing to their right wing that the nation's independents and centrists will laugh it off. As Thursday's events proved, nothing is guaranteed.

Rep. Vern Buchanan, R-Fla., a member of the House Ways and Means Committee, said Friday morning he believed Boehner was "very close" to having the necessary votes for passage the second time around.

"I'm confident the speaker will get there today," he said in an interview on MSNBC. Buchanan said conservatives have been wary of the various rival debt-limit bills because "people don't trust the process."

Nevertheless, Buchanan said "there's been some momentum" in Boehner's direction since late Thursday and into the day. He said he'll vote for the bill, but warned, "The bottom line is, we're willing to raise the debt ceiling, but at the same time we want to make sure the cuts are delivered."

The main area of dispute between the two parties is how to encourage or guarantee big spending cuts in the future without rekindling a fiercely divisive debt-ceiling debate such as the one now raging.

Interviews with well-placed insiders suggest the following road map, assuming Boehner can get his bill out of the House:

The Democratic-controlled Senate would kill it quickly. The focus then would fall on the Senate's two leaders, Reid and McConnell. They must decide whether they can reach a compromise that can pass the Senate — where a united GOP can kill bills with filibusters — and then pass the House and be signed by Obama. The White House would be integral to such talks.

Republican officials say McConnell could hold a strong hand, despite the House's shaky performance. He could argue that the House finally passed a bill to raise the debt ceiling, while the Senate has done nothing but kill that bill. If Tuesday's deadline passes with no resolution, Republicans say, voters will blame Democrats.

Under this thinking, the Senate would pass a measure similar to the House bill, perhaps with minor changes to save face and give political cover to Democrats who vote for it. The House would quickly concur, with numerous Democrats and all but the most conservative Republicans voting aye. Obama would have no choice but to sign it.

Democrats say the opposite is true. Obama has persuasively argued in recent weeks that Republicans are unreasonably demanding, they say.

Democrats control the Senate and White House. If Republicans insist that a partisan, House-passed bill is the only vehicle, then public anger will fall on them, this thinking goes.

The biggest sticking point is the House bill's call for congressional votes to raise the debt ceiling, in two stages, before the 2012 elections.

A $900 billion debt-limit hike would come first, coupled with $917 billion in spending cuts over 10 years. A second vote, late this year or sometime next year, would allow another $1.6 trillion in borrowing power, provided that Congress and the president have agreed to another round of spending cuts of that amount or more.

Obama has consistently rejected this condition. He says it would hurt the economy and touch off another ferocious political fight over the debt ceiling, which Congress previously raised with little fuss year after year. Global markets and investors would not be reassured by such a drawn-out, uncertain scenario, he says.

The White House says the prospect of an economically devastating default must not be used as the "trigger" to force Congress to cut the deficit. Such triggers would take effect automatically if Congress did not act on a prescribed deficit-reduction package.

Those could include deep cuts in programs such as Medicare and Medicaid, which would be painful to Democrats, and tax increases that Republicans would be loath to accept. But Republicans believe the threat of default is a much stronger incentive to shrink the deficit.

Presidential adviser David Plouffe told MSNBC on Thursday that the Republican House bill would "have this whole debt ceiling spectacle, three-ring circus ... repeated again a few months from now, over the holidays. You know, the debt ceiling debate would ruin Christmas."

If the House sends Boehner's bill to the Senate, a crucial point in the end-game scenario will come when McConnell decides whether to insist on the House proposal to raise the debt ceiling in two steps, both tied to large mandatory spending cuts. If he does, then Reid and Obama will have to decide whether to swallow the demand or let the impasse last beyond Tuesday, and blame McConnell.

Or, McConnell could yield. He could help pass a Senate bill that lets the second debt-ceiling hike take place more easily, with an incentive mechanism for spending cuts that stops short of a mandate.

That would hand a tough choice to Boehner. His tea party conservatives would howl in protest. It's possible that 100 or more of his 240 House Republicans would vote against such a Senate-passed bill.

The measure presumably would pass anyway, with ample Democratic votes. But Boehner's hold on the speakership could be weakened.

Of course, little or none of this might transpire if the House can't figure out how to pass a bill. In that case, Obama would seem to hold almost all the cards.