Richard Drew, Associated Press
Trader Timothy Nick works on the floor of the New York Stock Exchange Wednesday, Oct. 2, 2013.

The stock market rallied slightly on the first day of the government shutdown. The increases came despite the possibility that the government shutdown may "put as many as 800,000 federal employees out of work temporarily and cost the U.S. at least $300 million a day in lost output at first," according to a Bloomberg report.

Experts tell CNBC the markets aren't too bothered by the shutdown because investors think it is a temporary situation, and historically, the economy has done well after such shutdowns.

"History tells us it is not necessarily a bad thing for investors," Jeff Kleintop, chief market strategist at LPL Financial, told CNBC. "The 16 government shutdowns over the past 40 years that have ranged from one to 21 days have not been particularly negative for stock market investors, averaging only a 2 percent decline for the S&P 500."

"More importantly, from a longer-term perspective they preceded above-average returns," Kleintop added. "The S&P 500 Index has risen 11 percent on average in the 12 months following the shutdowns, above the 9 percent for all periods. Notably, in the last government shutdown that took place 17 years ago in late 1995, the S&P 500 rose 21 percent in the following year."

But some think the shutdown could be substantially harmful to the American economy. According to Peter Grier at the Christian Science Monitor, some analysts think it could impede the fragile economic recovery the country is currently experiencing.

"For each week the government is closed, fourth-quarter GDP would shrink by 0.2 percent, according to Nariman Behravesh, chief economist at IHS/Global Insight in Lexington, Mass.," Grier wrote. "A lengthy two-month shutdown would probably push the United States back into a recession, according to Moody’s Analytics chief economist Mark Zandi."