WASHINGTON – House GOP leaders won narrow approval of a plan to raise the federal debt limit Friday after revising the measure to appeal to rebellious conservatives. But the bill was rejected 59-41 in the Senate, where lawmakers were pursuing a separate, bipartisan agreement to avert a national default.

Heading into the final weekend before the Treasury expects to begin running short of cash to pay the nation’s bills, Senate Majority Leader Harry Reid, D-Nev., was poised to forge ahead with his own proposal to grant the Treasury additional borrowing authority. This would set up a crucial vote in the Senate shortly after midnight Saturday.

Democrats conceded that they still lack the votes to repel a filibuster threat from GOP senators. But Reid beseeched his Republican counterpart, Minority Leader Mitch McConnell of Kentucky, to join him in reworking the Democratic measure so the Senate could pass it and send it back to the House before slumping financial markets open Monday morning.

“The last train is leaving the station, and this is a last chance to avert a default,” Reid said in a speech on the Senate floor. He argued that the House bill would force Washington to endure another economy-rattling fistfight over the debt limit within a few short months.

“I say no, not again will we fight another battle like the one in which we are now engaged,” Reid said. “But default is not an option, either. And we cannot wait for the House any longer. I ask my Republican friends, break away from this thing going on in the House of Representatives.”

Though several Republican senators said a bipartisan compromise presents the only logical way to break the weeks-long stalemate, McConnell’s immediate response was not encouraging. In a written statement, he praised the House for passing “its second bill in two weeks that would prevent a default and significantly cut Washington spending,” and he criticized the Senate for “ginning up opposition.”

Still, Senate Democrats said they had received “positive signals” from Republican leaders. And though there were no formal talks with McConnell, Democratic leadership aides said they were hopeful that Reid would soon unveil a measure that would win Republican support.

Before the House vote, President Obama made a televised plea for compromise, arguing that the two parties are not “miles apart” and that he was prepared to work “all weekend long until we find a solution.”

Maine Reps. Chellie Pingree and Mike Michaud said in separate statements issued before the House vote that they would join other Democrats in opposing the revised plan from House Speaker John Boehner, R-Ohio.

“I am willing to make cuts,” Michaud said, “but I will not support a one-sided approach. This bill … contains no shared sacrifice, and it asks absolutely nothing of major corporations or the millionaires and billionaires that currently benefit from a system tilted in their favor.”

Michaud, who represents Maine’s 2nd District, said that “I’ve heard from thousands of Mainers that want a balanced deal reached, but not one that could lead to the slashing of critical programs like Medicare and Social Security.”

Pingree, who represents Maine’s 1st District, compared the debt ceiling debate to a “hostage negotiation, and working Americans are being made to pay the ransom. It’s time to put the partisan politics aside and pass a simple up or down vote on raising the debt ceiling, just like it’s been done dozens of times.”

Maine Sens. Olympia Snowe and Susan Collins joined most other Senate Republicans in voting against tabling the House bill.

Snowe said in a written statement after the vote that the Senate should at least have been allowed to consider the House GOP plan, but added that “hopefully now all sides will work together in an expeditious manner to work out the issues and bring us closer to agreement.”

“Time is of the essence,” Snowe said, “and the moment has long since arrived for shelving politics and instead striking the right policy. I do find it rather ironic that for this entire year, this Senate, described as ‘least productive’ at a time that coincides with one of the most challenging economic periods of our nation’s history, has done nothing substantial, rejecting numerous opportunities to pursue policies important to our job creation, boosting our economy and doing what is right for the fiscal stability of our nation.”

Collins, who has backed the bipartisan “Gang of Six” Senate plan that would mix spending cuts with new tax revenues, said she doesn’t agree with everything in the House bill.

But “it is essential that Congress pass legislation that averts a default, reins in spending, and imposes budget constraints,” Collins said. The House bill “would accomplish those overall goals.”

Both the House and Senate bills call for cutting deeply into agency budgets over the next decade and creating a new 12-member committee tasked with identifying trillions of dollars in additional cuts by the end of this year. Reid’s bill would extend the $14.3 trillion debt limit into 2013, however, while the bill from Boehner would give the Treasury a reprieve only until February or March. If the committee failed to come up with $1.8 trillion in savings, Boehner’s bill would force another battle over whether to grant the Treasury additional borrowing power.

In brief White House remarks, Obama noted that the two sides are “in rough agreement” about the size of the first round of spending cuts and that “the next step” to rein in borrowing should be a debate over “tax reform and entitlement reform.”

“If we need to put in place some kind of enforcement mechanism to hold us all accountable for making these reforms, I’ll support that, too, if it’s done in a smart and balanced way,” Obama said.

Talks have been under way for weeks about how to structure a plan so that both parties are encouraged to engage seriously in negotiations over future debt reductions. One approach would be to require tax hikes and across-the-board spending cuts — which would be unattractive to many lawmakers — if the committee refuses to come up with recommendations for added savings.

On Friday, Sen. Richard Durbin, D-Ill., the second-ranking Democrat in the Senate, said the design of that mechanism “is what all the negotiations are about. That’s going to be part of the end game.”

Without such an agreement, Obama warned that the United States stands to lose its sterling AAA credit rating — “not because we didn’t have the capacity to pay our bills. We do. But because we didn’t have a triple-A political system to match our triple-A credit rating.”

Obama again urged Americans to contact their representatives, clogging Capitol Hill switchboards for a second time this week. The White House also tweeted a number of Twitter handles for Republican lawmakers so voters could press them to “get past this.”

The president’s lobbying campaign appeared to have little effect in the House, where attempts by Boehner to move toward the center were forcefully rebuffed. Earlier this week, Boehner unveiled a measure drafted largely by aides to Reid and McConnell, but he was forced to yank it from the floor late Thursday when his right wing refused to fall in line.

For the next 23 hours, neither Boehner nor any other Republican leader issued a formal statement or paused in the Capitol hallways to explain to reporters what had happened.

Then Friday, Boehner rewrote the bill to prevent an increase in the $14.3 trillion debt limit unless both chambers of Congress approve an amendment to the Constitution to mandate a balanced budget. The change swayed a handful of holdouts, and the measure passed 218-210, with every Democrat and more than 20 Republicans voting no.

But the episode was a humiliation for the new speaker and his leadership team, demonstrating they lacked clout inside their own conference. Even their allies in the Senate were stunned.

On Friday, Boehner won tepid applause as he spoke in favor of the measure and defended his earlier effort to cut a far-reaching debt-reduction deal with Obama.

“I stuck my neck out a mile to try to get an agreement with the president of the United States. I stuck my neck out a mile. … But a lot of people in this town can never say yes,” Boehner said. “Yes, people can be critical of what we’ve done, but where are the other ideas?”

“I think things are moving better than they appear to be moving,” said Sen. Johnny Isakson, R-Ga. “There’s agreement on cuts. And there’s almost unanimous knowledge that default is not in the cards. That’s the heart of the issue. The rest of it’s details.”