Washington (CNN) -- President Barack Obama and House Speaker John Boehner both want talks to continue on ending the partial government shutdown and avoiding a possible debt default -- a welcome development after weeks of acrimony, if not proof a breakthrough is near.
Spokesman for both leaders, who were trading pointed barbs until a few days ago, issued statements after a Friday afternoon phone call, that "we should all keep talking." Conversations on Friday did yield some points of agreement among lawmakers, including on altering Obama's signature health care reforms and raising revenue to prevent forced cuts in government spending.
But overall, there has been little indication that there is any legislation yet that all the key players -- the President, the GOP-led House and the Democratic-led Senate -- will rally behind.
Much of the discussion of late revolves around a proposal from House Republicans to increase the federal borrowing limit for about six weeks to avoid a potentially harmful default as soon as October 17, when the Obama administration says the government will run out of money to pay its bills.
Republicans like Rep. Peter Roskam of Illinois say a temporary debt ceiling hike will allow all parties to "concentrate on the continuing resolution." His chamber could vote on the measure as soon as this weekend.
But the lack of a mechanism to immediately reopen the government -- which has been partially shut down since October 1, prompting the furlough of hundreds of thousands of workers, the closing of national parks and an increase in public anger -- could turn off some Democrats.
At the White House, press secretary Jay Carney repeated Obama's position that the partial shutdown must end before budget talks aimed to address the debt begin.
However, he didn't close the door completely on the House GOP plan, saying Obama would sign a temporary debt ceiling increase "as a bare minimum" as long as Republicans didn't attach partisan policy issues to it.
Sources: GOP senators losing patience with House
Meanwhile, Obama continued his outreach on Friday, including conversations with nearly 150 business leaders and 25 governors. He also reached across the aisle to Senate Republicans in a meeting Carney characterized as constructive, without offering details.
Some GOP members in the Senate have floated a plan discussed on Friday afternoon by a bipartisan group of about 10 senators, led by Republican Sen. Susan Collins of Maine and Democratic Sen. Joe Manchin of West Virginia, according to sources familiar with the meeting.
The proposal, which has yet to be introduced, would raise the debt ceiling and reopen the government with some qualifications. Among them: A Republican priority, backed by many Democrats, to end a tax on medical devices created by the Affordable Care Act, commonly known as Obamacare.
While much of their fire has been aimed at Democrats, some Senate Republicans also see their House colleagues as part of the problem.
There is growing concern being expressed in private meetings that the House GOP plan extending the debt ceiling for six weeks would come back to haunt the party, because it would expire close to the holidays, hurting retailers.
There also are worries about the impact of the partial shutdown dragging on, especially with polls showing the Republican Party getting the brunt of the blame.
Several GOP senators told CNN they will give House Speaker John Boehner a bit more time -- about 24 to 48 hours -- to reach a deal with the White House to raise the debt ceiling and reopen the government. But after that, they'll push the plan backed by moderate Senate Republicans more aggressively.
After Friday's meeting at the White House, Collins said Obama "listened carefully" and "said that some of the elements were issues we could work on. But he certainly did not endorse" the proposal.
Conservative Sen. Orrin Hatch of Utah said Obama called the medical device tax a "legitimate concern" that can be addressed because it wasn't part of the core Obamacare program.
According to other senators in the meeting, another Obamacare alteration under discussion would change the definition of a part-time worker in order to protect employees having their hours cut so businesses can avoid a requirement to provide health coverage.
Some conservatives -- like tea party favorite Sen. Ted Cruz of Texas -- left the meeting upset at Obama for continuing to insist the government must reopen and the debt ceiling must be increased before he would take part in full-fledged negotiations on deficit reduction.
"There was an awful lot of talking but the president still says he won't negotiate," said Cruz, who spearheaded the attempt last month to add anti-Obamacare amendments to a spending plan needed to prevent the government shutdown.
Source: Obama, Ryan exchange shifts tone
Even as he has continued to firmly repeat his positions, President Obama has been reaching across the aisle this week.
One potentially pivotal meeting came Thursday evening, when House GOP leaders went to the White House.
The two sides went around and around for an hour, getting nowhere. Then -- as first reported by CNN's Deirdre Walsh and Dana Bash, citing multiple attendees -- an exchange between GOP Rep. Paul Ryan and Obama seemed to clear the air.
CNN Chief National Correspondent John King told CNN's "New Day" that Ryan, the Republican chairman of the House Budget Committee, "said something to the effect of, 'Look, we know you don't like our position, we know you probably don't respect our position, but we're the Republican majority.' "
Those comments changed the tone of the meeting, King said. Obama reiterated his opposition to negotiations before the government reopens, then urged GOP leaders to go ask their colleagues what they want done to make that happen.
Republican Rep. Steve Southerland of Florida said the interaction between the two men -- who squared off in the 2012 election, when Ryan ran as his party's vice presidential nominee -- "was an important part of the conversation."
"Paul and the President certainly have a past through the last election, and I think there's a great respect between them. And you can't make that up." Southerland said.
The new atmosphere was reflected in both sides' comments after the meeting. The White House called it good and said the parties discussed "potential paths forward." GOP Rep. Hal Rogers of Kentucky said they were talking "in good faith" about both the debt and reopening the government.
"We're all working together now," said Rep. Pete Sessions, a Texas Republican.
In a video message to a right-wing political summit on Friday, Ryan noted conservatives can't get everything they want with Democrats holding the White House and a majority of the Senate.
"This President won't agree to everything we need to do," said the message from Ryan, according to excerpts provided by one of his aides. "A budget agreement with this President and this Senate won't solve our problems. But I hope it's a start."
CNN's Alan Silverleib, Chelsea J. Carter, Paul Steinhauser, Jim Acosta, Barbara Starr, Ted Barrett, Dan Merica and Brianna Keilar contributed to this report.