Remember the whole “tax on bullshit” concept? Basically, Alex Tabarrok and Robin Hanson argued that people would be less likely to spout out things that they didn’t even believe with high certainty if they had a little skin in the game.
The government shutdown is a similar tax on bullshit. It puts a mild amount of pain on a lot of people. If those people start saying, “Screw it, the congressmen on ‘my side’ should concede on the points I ostensibly agree with to spare me this pain,” well, then, that puts an upper bound on how strongly they believe those points.