Members of Congress should work without pay during a government shutdown because those people are the ones who caused the shutdown in the first place. Going without a paycheck also proves to the person's constituents that they mean business and are there for voters. People volunteer their time constantly for the betterment of humanity, so there is nothing wrong with members of Congress doing the same for voters.
Yes, If the congressan give up their check then when the government comes back they will be trying as hard as they can to make sure that this does not happen ever again, and try to make sure that they can get the government back on the right track to wealth.
If congress people want to cause a government shut down over something as simple as the debt ceiling and take food out of the mouths of other government workers' children, they, too, should be subject to these pay check freezes. Maybe they'd feel the pain they cause all the others involved in this.
Why should they be getting paid when their actions have cost others their pay. I think if a policy was put into place that took away congress' pay during a shutdown, it may very well cause them to get their poop in a group and figure out how to run our great country instead of being so damn stubborn. Sometimes in life you have to compromise, whether you like it or not.
When there's a government shutdown, all non-essential parts of the government must be shut down, with funding withheld. Considering their behavior during the last extended shutdown, I can't think of any part of government more worthless and non-essential than the United States Congress. So yes, take their paychecks away, too.