In exchange, Republicans want a commitment from the White House to negotiate a longer-term budget plan that would reopen the government.
Still, plenty of uncertainty is swirling around the fate of the federal government, which has been closed for 10 days and ground many essential functions to a halt.
Meanwhile, a stampede of business interests joined Treasury Secretary Jack Lew on Capitol Hill Thursday to issue dire warnings about the consequences of failing to raise the debt ceiling, which includes a plunge back into a recession and a precipitous rise in interest rates.
National Association of Realtors President Gary Thomas said failing to act would rapidly erase any gains in the fledging housing recovery.
"A default would be devastating for homeowners whose largest asset would lose value and equity, for homebuyers who would see dramatic increases in interest rates and tighter credit standards, and for entire communities that are still grappling from the impact of the financial meltdown,” Thomas told the Senate Banking Committee Thursday.
Thomas said that even a 1 percent increase in mortgage rates could lead to 450,000 fewer home sales and price many middle-class Americans out of the housing market.
Frank Keating, American Bankers Association president and CEO, said Thursday that a "ordinary Americans would bear the brunt of the damage if the United State defaults for the first time in history."
“If our nation defaults on its nearly $17 trillion in debt, the harm is likely to be measured in hundreds of billions of dollars,” Keating told the Senate Banking Committee.
"Even the slightest uptick in Treasury rates would cascade through the economy," he said.
"It would raise the cost for taxpayers to service our country’s debt and would raise the cost of borrowing for businesses, meaning job losses and price increases."
Credit unions also expressed concern in a letter to the Senate Banking panel on Thursday.
Dan Berger, head of the National Association of Federal Credit Unions (NAFCU) said "it remains critical that action is taken to resolve the debt limit issue in a timely manner."
"As evidenced by the still struggling housing market, the country’s economic recovery remains extremely fragile," Berger wrote.
"Failure to address the debt ceiling would threaten growth and recovery, deter investor confidence in the United States and breed uncertainty on a global scale."
While the markets bounced back, one economic indicator reflected the problems that could emerge in the coming weeks from the shutdown.
The government has released very little economic data since its operations were shuttered more than a week ago, but a report Thursday showed that first-time claims for jobless benefits jumped to their highest level in six months last week — up 66,000 to 374,000 — the highest since Hurricane Sandy hit last October.
The main reason for the cause was an upgrade in California's computer system that helped erase a backlog.
But the uptick, which neared levels that lead to greater concern for economists about the broader job market — may show increases in coming weeks from government employees and contractors who applied for unemployment benefits while their pay is frozen.
If any of those workers receive back pay, they would have to return any benefits they receive. But it is likely to ripple through the data and make it more volatile than normal.
In addition, the Bureau of Labor Statistics was unable to produce jobs figures for September, leaving the markets and many businesses without some crucial economic guidance.