The White House says there is still no agreement with Republicans in Congress on a possible solution to end the partial U.S. government shutdown and avert a government debt default.
Obama met with Senate Republicans, and late Friday he called Republican House Speaker John Boehner to discuss where negotiations stand.
White House press secretary Jay Carney, and Boehner's office, said they agreed only that "all sides need to keep talking."
Saying no agreement is at hand, Carney said the "constructive approach" Republicans had taken in recent talks indicated they understand the need to remove the threat of default from the process.
"The president's position that the United States, should not, and the American people cannot, pay a ransom in exchange for Congress doing its job remains as true today as it has been throughout this period," he said.
Earlier, Susan Collins, Republican senator from Maine, said talks with the president were "good but inconclusive," and Republicans raised concerns about the need to deal with the nation's $16.7-trillion debt.
"At least he is talking to members of Congress on both sides of the aisle. He may not want to call it a negotiation. That is what I would call it, and I do view that as progress," she said.
Congressman Xavier Becerra, a key House Democratic leader, said he hopes pressure on Republicans will bring a clean vote in the House of Representatives to reopen the government.
"Perhaps through the sheer force of the American people talking to Republicans and Republican leadership that have resisted a clean vote on the House floor," said Becerra.
Reports quoting lawmakers and aides said Republicans offered a short-term, six-week debt limit increase, to be followed by negotiations to fund the government.
That would be problematic for Obama, who has insisted that the federal government be completely reopened without ideological demands attached.
A package also could include steps to ease the sequester, mandatory budget cuts, which Republicans and Obama have said are harming the economy.
Carney said Obama has always been eager to engage in wider deficit reduction talks, but the need now is to resolve the government shutdown and default threat.
"Then we can move on to broader negotiations over how we achieve our budget priorities," said Carney.
On Capitol Hill, House Majority Leader Eric Cantor said Republicans hope the White House will continue to evaluate the offer they made, adding they remain hopeful that there is intent to resolve the impasse.
Efforts by House Republicans to defund President Obama's new health care law led to the partial government shutdown, which if it is not resolved will be two weeks old this Monday.
The ideological battle played out elsewhere in Washington as conservative Republicans addressed the Value Voters Summit.
One of them was former 2012 Republican vice presidential candidate Paul Ryan, who chairs the House Budget Committee.
"We need to completely re-think government's role in our lives. We need to completely rethink government's role in helping the most vulnerable. We need to completely rethink government's role in health care. That means we can never give up on repealing and replacing Obamacare," said Ryan.
Asked about next steps, the White House spokesman would only repeat that Obama believes all sides need to continue talking to reach "an agreement of some kind" to reopen the government and remove the threat of default.
Watch related video story by VOA's Carla Babb