IMO, this actually wouldn't be the worst thing in the world. IIRC, Trump is the one behind the scenes pushing for the shutdown. If they bring him front and center to do the same thing, he will make it about him and his criminal investigations instead of anything tangentially fiscal or populist, which could take the air out of the need to do it.
I don't see Trump stopping because millions are suffering either. It'll be terrible for our democracy in the short term, but hopefully in the long run it's the random thing that actually turns the tides on his approval.
The one downside is that Republicans seem to have less to sacrifice, so they will likely hold the US hostage for something that Dems really believe in, such as immigration or Ukrainian aid, either of which will become a talking point about Dems selling out their people and incentivize short-term thinkers to become more apathetic.