Updated 6:19 p.m. | The White House pushed strongly late Friday for a longer-term extension of the debt limit than House Republicans have offered as they continue to negotiate a deal that would reopen the government.

White House Press Secretary Jay Carney called the talks “constructive,” but he sharply criticized the six-week proposal on the table as one that would increase uncertainty heading into the holiday season. And Carney rejected the GOP proposal to tie the debt ceiling to broader budget talks.

“In relation to the proposal that has been discussed in the press, it is our view that we cannot have a situation where the debt ceiling is extended as part of a budget negotiation process for only six weeks, which would put us right back in the same position that we’re in now,” Carney said.

He also repeated assertions that President Barack Obama would not pay a “ransom” to reopen the government.

A spokesman for Speaker John A. Boehner said Friday afternoon that a final package has not yet been nailed down.

“The President and the Speaker spoke by telephone a few minutes ago,” said the Ohio Republican’s press secretary, Michael Steel, in a statement to reporters sent out shortly before 4 p.m. “They agreed that we should all keep talking.”

House Majority Leader Eric Cantor, R-Va., leaving the Capitol on Friday, expressed optimism that the White House would agree to the GOP’s offer.

“I am hopeful that the White House will continue to evaluate the offer we made and we remain hopeful that there is intent on both sides to resolve the impasse,” he said.

Carney repeatedly dodged questions about whether the talks constituted “negotiations” that the president and Senate Majority Leader Harry Reid, D-Nev., have vowed not to engage in until after the government is open.

He noted it would take much longer than just the next couple of days to reach a comprehensive budget agreement.

Senior GOP lawmakers went to the White House on Thursday afternoon prepared to pitch a six-month debt limit increase in exchange for a promise to engage in good-faith budget talks, but they left the meeting ready to find a way to pass a continuing resolution, too, with some concessions.

Republicans characterized Obama as exhibiting a new willingness to talk about possible gives-and-takes to resolve the current fiscal impasse, and they sent an informal offer back to the White House late on Thursday night.

The White House is apparently still weighing the options, while sources within House Democratic leadership indicated that House Republicans were not keeping them abreast on the status of discussions.

Republican Policy Committee head James Lankford of Oklahoma told reporters that there had been additional offers from both sides throughout the day. Members will likely be briefed on those offers at a Saturday morning conference meeting. If a deal is struck, a bill dealing with the debt ceiling and, possibly, government funding could then be brought to the floor. Alternatively, the House could decide to vote on pending legislation relating to the farm bill while discussions continue, resuming legislative business on Monday evening.

When Senate Republicans returned to Capitol Hill on Friday after their designated meeting with Obama, lots of talk centered on a proposal to raise the debt limit, fund the government at sequester levels for six months, and either repeal or delay by two years a medical device tax created by the Affordable Care Act, otherwise known as Obamacare. Sen. Susan Collins, R-Maine, is championing the proposal in her chamber, while Reps. Ron Kind, D-Wis., and Charlie Dent, R-Pa., are pushing a similar package in the House.

Some Republicans from both sides of the Capitol gathered in the speaker’s office on Friday afternoon. Budget Chairman Paul D. Ryan, R-Wis., indicated to reporters that he does not support the proposal pushed by Collins, Kind and Dent.

Matt Fuller, Steven T. Dennis and Niels Lesniewski contributed to this report.