"I've gone up to a 25-percent chance" of a government shutdown, said Potomac Research chief political strategist Greg Valliere. "Last month, I was at 10 percent. I think (House Speaker John) Boehner and most of the leadership know this could blow up on them in the 2014 election, and they're leery about doing anything that radical."
About 40 conservative Republicans revolted against Boehner's plan to move forward with a resolution that would have kept the government running while Congress grappled with the debt ceiling.
(Read more: Democrats bail on Obama as budget battle looms)
"That's the one (debt ceiling) the market has to worry more about," said Valliere, adding he thinks the GOP leadership will ultimately avoid hitting the ceiling and causing a first-ever government default. "But I cannot give you a coherent, concise way of how they finesse this. I think it will get dicey. ... Jack Lew threw down the nuclear weapon. He said if we don't get a debt ceiling hike, people may not get their Social Security checks and we may not be able to pay the troops. The Republicans are playing with fire."
Barry Knapp, head of equity portfolio strategy at Barclays, said it may be the Democrats' intent to trap the GOP in a negative position and raise the public ire, since the Republicans have an improving chance in the mid-term election next year. "I think this is the last hope for the Democrats to take back the House," he said, noting they could "make the Republicans fall into a trap, make a mistake and get blamed for shutting down the government."
Valliere said the House will probably pass a continuing resolution to fund the government, tied to defunding the Affordable Care Act, also called Obamacare. But it will not make it in the Senate, and the two sides will come to a stalemate.
(Read more: GOP in disarray overshutdown threat)
"I just don't see a government shutdown. I see a very small chance of a default. I think the chances are 50/50 that the Treasury could run out of money, and we would have a period of great uncertainty over what the Treasury could pay for," he said. "It's going to get to be early November before we get a debt ceiling deal. I think Treasury can limp through October but you're cutting it very close. The window of greatest market anxiety will be the last week of October, first week of November."
As for the market, it heads into October, a traditionally volatile month, with a possible fiscal crisis ahead. Knapp points out that during the fiscal calamities in the past couple of years, the Fed was either easing or moving toward more easing. This year the Fed may end up paring back its bond buying program, though it surprised Wall Street Wednesday by leaving its $85 billion monthly bond buying program in tact.
"I think (Fed officials) are very scared about ruining four years of work and especially with the shenanigans going on in the fiscal side of Washington, where these guys clearly don't care about people. They just care about which party is in power. I think that scared them as well," said Rich Bernstein, CEO of Richard Bernstein Capital Management.
(Read more: Taper off! Fed keeps foot on the pedal)
Washington will fight one less battle than expected this fall, since former Treasury Secretary Larry Summers dropped out of the running for Fed chairman. Although Summers was President Barack Obama's choice, Democrats and Republicans were lining up against him. Wall Street now sees Fed Vice Chair Janet Yellen as the likely candidate to replace Fed Chairman Ben Bernanke, but the White House has yet to confirm that.
"There's plenty of scope for volatility," said Knapp. "The market likely got the candidate they want to be the next Fed chairperson. You have all these things that already occurred, and the market is at its highs. What's the next positive catalyst? It's hard to see one."
(Read more: Gov't can't control spending addiction: Ron Paul)
Now the fiscal debate is moving to center stage. "This is just reigniting the whole dysfunctional government thing. If there is a catalyst for the correction that everybody's been calling for since the beginning of the year, this is the one credible possibility for it," said Art Hogan of Lazard Capital Markets. Hogan said the market could quickly see a 5- to 10-percent correction if Congress pushes the situation to the edge. It could be worse if the government is shut down.
—By CNBC's Patti Domm. Follow here on Twitter