It depends how long things go on of course, but one effect is that government contractors will earn less revenue this quarter than their previous guidance had suggested, likely causing a hit in their stock prices. Lockheed, Boeing, Northrop, IBM, Booz Allen, Leidos, etc, are all going to be hurt to varying extents. It's hard to tell if it will be felt in the broader market, but there might be some bargains to be had among that group in Q2.
Anyone depending on the government will probably put off larger purchases until it's over. I don't imagine many Federal employees are going out and buying new cars or houses or booking expensive vacations this weekend. If it's a short shutdown and almost everybody gets back pay, then that kind of spending will bounce back quickly. If it goes on for more than one pay period, then I think you're going to see less spending overall and unemployment will start spreading across all kinds of businesses in areas where there's a heavy government or military presence.