Republican Boehner has been at the center of multiple other similar struggles, with this one particularly testy heading into a presidential election year. Valliere thinks Boehner actually could act as a peacemaker on his way out the door. However, that atmosphere likely will change under his successor, expected to be Kevin McCarthy of California.
Read MoreBoehner: Leadership turmoil could do harm
"Boehner will go to (minority leader) Nancy Pelosi if he has to, to get votes from Democrats. What does he care? He's leaving," Valliere said. "It will be easier for him to get votes for a continuing resolution that lasts until Dec. 11."
While the congressional wrangling unfolds, Fed Chair Janet Yellen and her fellow central bankers will be plotting a way to escape seven years of zero interest rates.
In a much discussed speech Thursday, Yellen again indicated the Federal Open Market Committee was ready to hike its key funds rate before the end of the year. However, the FOMC only has two meetings left: one in October, when a hike seems highly unlikely for a variety of reasons; and the other in December, which would come just a week after the government shuts down.
Read MoreSo why all the fuss over what Yellen said?
"The risk of disruption to the economy and/or financial markets from another debt ceiling standoff is another reason to suspect that the Fed definitely won't hike interest rates in October and possibly may even stand pat in December, too," Paul Ashworth, chief U.S. economist at Capital Economics, said Friday in a note to clients.
For investors, that means likely more volatility as market participants continue to be left guessing by the course of Fed policy.
"If the markets hate uncertainty, there's real uncertainty looming in December because of the Fed angle," Valliere said. "The market will really start to pay attention to this story after Thanksgiving."