There is no legal way to "fire Congress" and destroying the fabric of our government would not be worth the gains we would get from "firing Congress." The closest we can do is for people to not re-elect their own Senators or Representatives.
The problem with this is that Congressmen like Ted Cruz who are breaking Congress are liked by their constituents who, apparently, enjoy things like Republicans shutting down the government. As long as men like Senator Cruz keep getting elected we have no hope of a functional government.
Congress should not be fired as a whole. This would cause a huge strain on our country, to have to suddenly replace all of Congress, and would create a temporary hole in the three degrees of checks and balances (legislative, executive, and judicial). However, we should remember that we are the ones who hire our Congressmen and women, so we should always be sure to use our voting privilege in order to choose who we want to represent us. In that way, we do hold the power to "fire" individuals who are not doing what they were hired, or voted in, to do.