I am sure that it will. I am also sure that many Republicans who oppose government services will see this as a benefit of the shutdown. Who will want to work for the government and take the risk of not getting paid? It will be much harder to get talented people to work for the government. I was a federal employee for almost 38 years and thought it was an excellent place to work with dedicated employees doing their best to help the public.
This is in addition to the long-term damage Trump has done to the State Department and the EPA. He doesn’t believe in the mission of either one. It will be hard to rebuild them after he is gone now that people see their work can just be thrown away if someone like Trump is elected.