On Tuesday, some Senate Democrats were discussing a bill that would stretch funding through Nov. 15 instead of mid-December, a move that would condense the battle time.
House Republicans on Friday passed a resolution that would fund the government but also defund Obamacare. The vote came after about 40 conservative Republicans revolted against House Speaker John Boehner's plan to move forward with a resolution that would have kept the government running while Congress grappled with the debt ceiling.
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"I think there will be a face-saving deal. It may not come until Monday night because it is Washington," said Valliere. "Even if there is a shutdown, I think it would be brief and would not be the end of the world. We're a long way from the debt ceiling. The debt ceiling could become a crisis in the next couple of weeks. The White House is saying they absolutely will not negotiate."
Republican leadership in the Senate has rejected the idea of tying the funding legislation to defund Obamacare. Sen. Ted Cruz, R-Texas, sought to get fellow Republicans to support the House plan but GOP Senate leaders lined up against it Tuesday.
The Senate is now expected to vote over the weekend on a "clean bill' addressing only the continued funding of the government.
(Read more: McConnell breaks from tea party on Obamacare vote)
"I think we probably do get the Senate to pass the extension to December 15, without stripping funding for Obamacare, and then it gets kicked back to the House," said Jeff Kleintop, chief market strategist with LPL Financial. He said it is likely to pass the House after some maneuvering by Boehner and the Republicans will save the big fight for the debt ceiling.
Kleintop said the market's losses since Friday appears to be in part a reaction to Congress. Stocks were slightly higher Tuesday afternoon.
"I think we've seen some of that in the last few days. The question is: 'Are people already maybe today starting to buy the rumor of a deal getting done in the 11 hour?' We didn't see all that much of a selloff. We've been through this so many times. Congress crying wolf again and again," Kleintop said.
Kleintop said that the market may not have had a bigger reaction to the threat because the last two shutdowns were not particularly negative for stocks. They were also brief shutdowns—five days in November 1995 and 21 days in January 1996. "(The market) was basically flat. It wasn't such a big deal. It was expected to be temporary, and there wasn't a debt ceiling debate coming after," he said.
Kleintop said House Republicans could bring some new chip to the table for the debt ceiling fight, and one big one could be the controversial Keystone XL Pipeline. President Barack Obama delayed approval of the pipeline, which would take oil from Canada to the Gulf Coast refineries.The pipeline is now awaiting State Department action.
Valliere said the feuding over the debt ceiling could get ugly, especially around early November when Treasury would be forced to figure out which bills the government could pay. "There may be vendors that don't get paid. There could be a rocky period in early November in terms of what the Treasury could pay," he said.
"I don't think there's a threat of default, but I do think this would be a headwind for the overall economy. If we go through a stretch where it's unclear what the government is going to be able to pay for, it would be a psychological negative for consumers, for investors and for companies," said Valliere. "The end game is unclear."
Kleintop said the battle would probably draw in the ratings agencies again, particularly if it looked like there was no deal on the debt ceiling.
"If there is an imminent threat of default I think the president would consider raising the debt ceiling by executive authority. He was counseled in 2011 by constitutional scholars that he had a right to do this," said Valliere. "I know the White House is leery of that, and it would lead to litigation, but if faced with an imminent default that option would be on the table."
—By CNBC's Patti Domm. Follow her on Twitter