"The real question is if we reach the same conversation around the debt ceiling. America defaulting [would have] a greater impact than the short-term impact on markets from the [budget] conversation we're having right now," Ford told CNBC on Wednesday when asked whether a government shutdown was a realistic prospect.
(Read more: Congressional shutdown fight is nothing. Stay tuned)
The Treasury has said the U.S. debt limit of $16.7 trillion will be hit in mid-October, with Treasury Secretary Jack Lew saying there is no plan in place to pay all of the government's bills once that threshold has been hit.
"The subdued tone to the markets right now is probably because of the debt ceiling, but I don't think we'll get such severe downward pressure that we got in 2011 with the downgrades to the U.S. credit rating," Geoff Lewis, global market strategist, at JPMorgan Asset Management told CNBC Asia's "Cash Flow" on Thursday.
"At the moment, it is all theatrics. I think the Republicans realize that if they disrupt government for no good reason, it could come back to haunt them in the next mid-term elections," he added.
On Friday, House Republicans passed a resolution that would fund the government until mid-December but not Obamacare – President Barack Obama's healthcare reform law.
"In the near term, the debt ceiling debate and the continuing [budget] debate is going to cast a cloud over markets and in this environment it is safe havens such as the yen and the Swiss franc that do okay," said Nick Verdi, director of foreign exchange strategy for Asia-Pacific ex-Japan at Barclays.
According to Chris Weston, chief market strategist at trading firm IG, there's one reason why investors should worry about a potential U.S. government shutdown.
"If we do see a shutdown, then subsequently government produced data will be held back from release, and thus we won't get the October 4 non-farm payrolls, which is so important to the taper jigsaw; clarity and uncertainty would get that little bit hazier," Weston said in a note.
(Read more: Taper tantrum to ruffle Asian bond markets, ADB warns)
The Federal Reserve last week took markets by surprise by not delivering a widely anticipated scaling back of its asset purchase program, leaving markets speculating once more about just when Fed tapering will begin.