Dollar bills are seen attached to a computer on the floor of the New York Stock Exchange.

Though some analysts are advising preparation in case of a default, investors thus far are treating that extreme set of circumstances as unlikely.

That scenario would lead to a downgrade of government debt and a likely stampede of U.S. bond selling, which in turn would trigger losses in money market fund—MMF—accounts.

Only if the U.S. failed to pay its bills over an extended term—say, longer than a month or so—would depositors in normally ultra-safe money market funds hit trouble, most experts say.

How safe is your money market fund amid the Washington chaos? Probably pretty safe, outside of a worst-case debt-default scenario.

"Any money market fund certainly has some level of risk. However, I would still say it's one of the safest asset classes out there," said Jerry Klein, managing director at Treasury Partners of HighTower Advisors in New York.

"When you look at the worst-case scenario ever, which occurred in 2008, investors lost 1 percent of their money in one fund," Klein added. "We could point to thousands of bank failures where people have been hurt in a much more significant way."

(Read more: Here are 7 debt-default doomsday scenarios)

Indeed, the showdown in Washington has kindled fears that Congress may not agree to raise the debt ceiling and ultimately will cause the U.S. to default on its debt obligations.

That in turn has conjured images of the 2008 financial crisis, during which a money market fund "broke the buck," meaning its net asset value turn negative and sparked an outflow of MMF money.

In the 2008 crisis, the Federal Reserve stepped in and guaranteed money market deposits. However, since the passage of the Dodd-Frank banking reform bill, the U.S. central bank would be prohibited from repeating that intervention.

Not to worry, though, say industry experts: The funds themselves have reduced their exposure to the short-term U.S. Treasurys that would be most at risk in case of default, and are prepared to steer themselves out of crisis.

(Read more: Is Washington cryingwolf over a default?)

Ratings agency Fitch said this week it "understands that many MMF managers have shifted out of US Treasury securities maturing in October that could be most at risk to a debt ceiling impasse."

Those encouraging words did come with a cautionary note: "However, a longer-term impasse could put pressure on of the ability of some MMFs to meet timely redemptions and maintain preservation of capital, consistent with Fitch's rating criteria for MMFs, which could have negative rating implications."

Investors in turn have shown modest concern but no signs of panic.

Over the past week investors pulled just shy of $20 billion from the $2.7 trillion money market pot, according to the Investment Company Institute.

That total was "well within the range that money market funds can easily accommodate," ICI chief economist Brian Reid said.

(Read more: US to the G-20: Debt ceiling impasse will end soon)

"The funds have been preparing their portfolios in anticipation of a possible default, taking necessary actions to make sure they have sufficient liquidity," Reid said in an interview.

Reid added that even funds that are focused on investments in government debt—as opposed to "prime" funds that have more diverse holdings—shouldn't suffer over the long term as Treasurys and T-bills ultimately will be redeemed at full value.

"If we use 2011 (the last debt-ceiling impasse) as a test case of what happens, the outflows from Treasury and government funds were about 7 or 8 percent of fund assets, which a money fund can easily accommodate," Reid said. "Everything that we've seen so far doesn't look like the flows have been materially different than they were in the debt ceiling debate we saw in 2011."

Of course, that could change in the event that the debt ceiling debate takes a turn for the worse, something that markets are not expecting.

"The bottom line is we're not seeing anything that's going to uniquely affect the money funds," Reid said. "If we do, they can pretty much (hold) in the near term."

—By CNBC's Jeff Cox. Follow him on Twitter @JeffCoxCNBCcom.