No, there has been only one set of elections where voters could respond to the shutdown. No other election is relevant with regards to public opinion on the shutdown.
As for evidence, I can't really say I know what you're asking for here. Election results are public record available on various government websites (depending on jurisdiction). Even Fox News is reporting these results.
If you're looking for an analysis of the election results, well, go to your news outlet of choice and look them up. Mississippi's Republican supermajority was broken this month. Mamandi, the DNC's (reluctant) choice, was elected mayor. CA prop 50 passed. The list goes on and on. I can't see a single person claiming this election was anything but a massive victory for the dems.