Politics at this point is something that only the rich really participate in, and congressmen have plenty of other sources of income. Particularly during times of economic hardship, politics should be something people do because they want to, not because they are being paid to, and if the government is so disenfranchised it needs to shut down, congressmen should not be continuing to get richer off tax dollars.
I absolutely think that we should be paying Congress during a shutdown. The last thing we'd want is for some lobbyists to weasel their way even further into the Capitol by offering corporate financial support (more so than they already get) during their self-imposed moment of crisis. However, we can make it more difficult for Congress to get their money by cutting off as much support staff as possible: Sorry, the payroll office is closed so we can't make a direct deposit into your account. Sorry, the cafeteria is closed so you'll have to hit up the Hardee's down the street (and no, you can't send an aide out for you, because they're at home not getting paid, too).