WASHINGTON — Negotiations between President Obama and congressional Republicans intensified Friday as lawmakers rushed to find an elusive agreement that would reopen federal offices and avert a default on the national debt.

With progress still slow in the House, Senate Republicans went to the White House, where Maine Sen. Susan Collins presented a plan that would end the government shutdown and extend the debt limit through January, but would also delay a medical device tax included in the Affordable Care Act.

Collins’ plan was one of several discussed during the more than 90-minute meeting, but by Friday evening the framework of her proposal was emerging as the top Senate Republican plan. Senators said Obama listened politely to the proposals by Collins and others but did not specifically endorse any.

Collins’ plan would continue the automatic sequester cuts but allow more flexibility in how they can be applied.

Senior Republican senators urged House Speaker John Boehner of Ohio to join them in supporting the measure, according to The Washington Post.

By late Friday, Senate Republicans – led by Collins, Kelly Ayotte of New Hampshire and Lisa Murkowski of Alaska – sent draft language to their Democratic counterparts, the Post reported.

“The president obviously wants to get this resolved and certainly isn’t dismissive of it,” Sen. John McCain, R-Ariz., said of the proposal put forward by Collins. McCain is one of a group of senators working with Collins on the plan. “But he has his positions, which are well known.”

McCain added, however, that the sides were still “a long way” from a final agreement.

Collins told reporters the president expressed interest in aspects of her plan but had not endorsed any proposals. She described Friday’s conversation as constructive. But, she said, “I’m concerned we still don’t have an agreement on a specific plan.”

White House spokesman Jay Carney also suggested that the conversation with Senate Republicans had been productive but that the president had not pledged support for any single plan. He also reiterated the president’s position that Republicans cannot “demand a ransom from the American people in return for not defaulting.”

“I would say that a number of lawmakers in the Senate as well as the House have expressed views that are constructive, in our estimation,” Carney said during his daily press briefing when asked about Collins’ plan. “Senator Collins is one of them. But I’m not going to evaluate from here a specific proposal beyond what I’ve said thus far.”

Friday’s negotiations came on the 11th day of a partial shutdown and less than one week before Oct. 17, which federal Treasury officials estimate is the final day they will have enough cash to pay all the government’s bills. Economists, business leaders and financial experts warn that defaulting on the national debt could have catastrophic consequences on the economy in the U.S. and around the globe.

Sen. Bob Corker, R-Tenn., acknowledged that he went into the White House meeting with somewhat low expectations.

“But I left there feeling it was very useful and constructive,” Corker said. “And it lent to sort of an understanding where the various camps are and, I think, an understanding of where the sweet spot might be to solve this problem.”

Although one of several proposals floated by both sides, Collins’ plan appears to be gaining favor among her Republican colleagues in the Senate. Collins said she is fielding increasing calls from Democrats interested in learning more about the plan, but Democrats remained quiet on the proposal Friday.

Sen. Barbara Boxer, a California Democrat, said she was withholding judgment until she learns more about the plan, which she said has not been distributed broadly.

“I hear different things about it, so I don’t want to comment until I see it,” Boxer said.

Friday’s meeting followed a much smaller gathering at the White House on Thursday night between Obama and House Republican leaders. Boehner and others laid out their proposal to extend the debt ceiling – the country’s $16.7 trillion borrowing limit – by six weeks, a time frame that Democrats have rejected as too short.

House Republicans are now developing plans to also end the partial government shutdown as part of a package that includes cuts in benefit programs. The Associated Press reported that Obama spoke to Boehner on the phone Friday after he met with Senate Republicans about their potentially competing plans to end the shutdown.

The spate of meetings along with encouraging statements from lawmakers buoyed hopes that the stalemate between Republicans, Democrats and the White House may be softening.

“Now we’re back here to actually work on trying to get a solution on a bipartisan basis,” Senate Minority Leader Mitch McConnell, R-Ky., said after returning to the Capitol, according to The Associated Press.

Hundreds of thousands of federal workers remain on furlough – and hundreds of thousands more are working without pay – because of the shutdown prompted by conservative Republicans’ attempt to link funding for government operations to the Affordable Care Act. House Republicans have passed numerous piecemeal approaches to fund specific government functions, but Democrats have rejected most of those.

Senate Majority Leader Harry Reid, D-Nev., has proposed lifting the debt ceiling by $1 trillion through the end of 2014 and may bring that bill up for an initial vote Saturday. But Republicans have said their caucus is unwilling to go along with such a large increase without concessions on spending.

The plan developed by Collins and other senators is a mix of previous proposals intended to win bipartisan support but that would require concessions on both sides. Several news reports suggested that Collins is also working with Democratic Sen. Joe Manchin of West Virginia, but a spokesman for Manchin declined to comment.

The current version would extend the debt ceiling through the end of January and reopen federal offices by funding the government for six months at an annual rate of $986 billion. That is a level that Republicans say is consistent with congressional budget controls and maintains the sequestration budget cuts.

Democrats, who want to end or replace the sequestration cuts, grudgingly agreed to the figure only recently. Collins’ plan would give federal agencies more flexibility to implement the cuts.

But the proposal also calls for delaying a 2.3 percent tax on medical equipment and devices included within the Affordable Care Act – a change from an earlier version that called for repealing the tax.

The Senate has already voted to eliminate the tax, which businesses strongly oppose and critics predict will cost jobs. The tax does not relate directly to the Affordable Care Act’s primary mission – to lower the number of uninsured individuals nationwide. But Democrats have since resisted Republican attempts to use budget negotiations to change the health care act.

The tax also helps finance the health care law, an issue that Boxer raised when asked about Democratic support for eliminating or delaying the tax.

“The most important thing to us is that it is deficit neutral and that it doesn’t bust the budget,” Boxer said.

Collins proposes to offset the $30 billion loss from repealing the tax by allowing companies with fixed pension plans to temporarily lower contributions to pension funds when interest rates are low in anticipation of higher rates later on. The “pension smoothing” would result in higher tax revenues to the federal government by lowering companies’ deductions.

Sen. Orrin Hatch, R-Utah, estimated that Collins’ presentation only took five or 10 minutes during the roughly 90-minute meeting at the White House on Friday. But Hatch said Collins “had done us all a big favor by having the courage to come up with” a proposal.

Asked if he believes the Collins proposal is the most likely path to an agreement, Hatch responded: “I don’t know about that. That’s just one of them.”

McCain predicted that some change to the medical device tax – whether a repeal or a delay – “will probably be part of any agreement” because both sides have opposed the tax in the past.

The round of White House meetings comes as Republicans are feeling more heat on the shutdown. A new Wall Street Journal/NBC News poll showed that 53 percent of respondents blamed Republicans for the government shutdown, compared to 31 percent blaming Obama. Just 24 percent of those polled had a positive view of the Republican Party, compared to 39 percent for Democrats. The poll suggests Obama’s standing with Americans has risen slightly.

McCain, who has been a vocal critic of House Republican strategy linking government funding to the health care act, called the polls “devastating” and said of his House counterparts, “I know they are reading the polls.”

“We do need to reopen government and we do need to deal with the debt limit,” Collins said. “I believe that the plan that I put forward is increasingly attracting interest from members on both sides of the aisle, based on what I am hearing.” 

Kevin Miller can be reached at (207) 317-6256 or at: kmiller@pressherald.comTwitter: KevinMillerDC