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Obama met Senate Republicans at the White House and spoke by phone to House of Representatives Speaker John Boehner as negotiations intensified on how to get hundreds of thousands of federal workers back on the job and extend the government's borrowing authority past the October 17 limit.
It was hard to gauge the progress of talks, as all sides refused to divulge many of the specific details of what is being discussed.
But both sides spoke with new optimism about the possibility of avoiding a fiscal crisis. Lawmakers were expected to work through the weekend with a goal of finishing a deal by early next week.
Economists have warned that a debt default would create global economic chaos, and analysts warned on Friday that if the shutdown lasts more than a month, it would cause a sharp slowdown in fourth-quarter economic growth.
Obama wants the debt ceiling raised for longer than the six weeks first proposed by Republicans, and Republicans want a commitment to broader deficit-reduction talks from the White House.
"The two of them agreed that all sides need to keep talking," White House spokesman Jay Carney told reporters after the call between Boehner and Obama. "It at least looks like there is a possibility of making some progress here."
House Republicans will meet at the Capitol on Saturday morning to discuss their options after sending the White House a proposal that included the short-term increase in the debt limit that would clear the way for reopening the government.
The House Republican proposal called for cuts in programs like the Medicare health plan for seniors to replace two years of the automatic spending cuts known as "sequestration" agreed to last year by Congress, senior aides said.
"The good thing is the negotiations are ongoing. That is much more progress than has been the case lately," House Majority Leader Eric Cantor of Virginia said.
But Carney said the short-term increase proposed by Republicans would not provide enough certainty for the economy and would put the country back on the verge of default during the end-of-year holiday season.
"A debt ceiling increase at only six weeks tied to budget negotiations would put us right back where we are today in just six weeks, on the verge of Thanksgiving and the obviously important shopping season leading up to the holidays," Carney said.
At a White House meeting with Senate Republicans on Friday, Obama expressed concerns the proposed debt-limit extension was too short and also talked about the need for new revenues as part of any long-term deficit reduction plan, Republican Senator Orrin Hatch of Utah said.
Large portions of the US government shut October 1 after Obama and Democratic lawmakers rejected House Republicans' demands for delays to Obama's healthcare reforms in exchange for temporary government funding. Thousands of government workers have been furloughed and parks and attractions shuttered.
Deals were struck on Friday to reopen three of the most famous landmarks, using state money and other funds. The Grand Canyon, Mount Rushmore and the Statue of Liberty will soon be open for visitors, as well as some parks in Colorado and Utah.
'A DIFFICULT EXPERIENCE'
Hatch said he left the meeting feeling the fiscal fight would still be a "difficult experience."
But Senator Bob Corker, a Republican from Tennessee, said senators "had to leave there knowing that probably in the very near future we will have these issues behind us."
The new sense of optimism sent US stocks higher on Friday, extending gains from a major rally in the previous session. But US Treasury bills maturing in late November and throughout December spiked as banks and major money market funds shy away from holding debt with any risk of delayed interest or principal payments.
"If the shutdown lasts through the end of October, the economic damage would be significant, reducing real GDP as much as 1.5 percentage points in the fourth quarter," said Mark Zandi, chief economist at Moody's Analytics in West Chester, Pennsylvania.
An unlikely coalition of the heads of the US Chamber of Commerce, AFL-CIO labor federation and United Way Worldwide joined together on Friday to warn about the dangers of a prolonged economic impasse.
"While we may disagree on priorities for federal policies and we even have conflicting views about many issues, we are in complete agreement that the current shutdown is harmful and the risk of default is potentially catastrophic for our fragile economy," they wrote in a letter to Obama and members of Congress.
Obama spoke by phone to a group of about 150 leaders of major businesses on Friday afternoon, the White House said.
"The president reiterated that his first order of business is to urge Congress to reopen the government and remove the threat of default, and then he is willing to engage with Congress on a long-term budget," the White House said.
Time was running short, with the shutdown in its 11th day and less than a week to go before the Treasury Department exhausts its ability to borrow money to pay the government's bills.
Any deal that is struck by leaders could face a revolt from rank-and-file conservatives in both the House and Senate.
Texas Senator Ted Cruz, a Tea Party favorite who has been a leader of conservatives demanding delays or defunding of Obama's healthcare law before they will approve a budget deal, took a hard line at a conference of conservative activists.
In a speech frequently interrupted by hecklers but warmly embraced by the smaller-government Tea Party faithful, he said the country must "stop that train wreck, that disaster, that nightmare that is Obamacare."
Senate Democratic leader Harry Reid is scheduled to hold a vote on Saturday on a measure giving a one-year debt ceiling increase without conditions. It is expected to be opposed by Senate Republicans. The chamber may then move quickly on a shorter time frame, even if it is not Democrats' first choice.
Senate Republicans were discussing a series of different ideas, including a quick reopening of the government coupled with a debt limit increase and the repeal of an unpopular medical device tax that would raise revenues to pay for the healthcare law.
Reid on Friday publicly criticized Republican calls for a short extension of the borrowing authority.
"We do not believe a six-week delay of a catastrophic default is enough to get the economy the confidence it needs," Reid said on the Senate floor.
A Reuters/Ipsos poll on Friday showed more Americans blamed Republicans for the shutdown, which also appears to be damaging the party's reputation on issues such as healthcare and the economy.
Nearly one-third of Americans - 32% - say Republicans are responsible for the shutdown, up from 26% a week ago. About 4% said Democrats were mostly at fault for the shutdown, down from 5%. Sixteen% blamed Obama, up from 14%.
