But the narrative in the fall of 2013 that the shutdown showed Republicans were a chaotic party that couldn’t be trusted in power certainly did not prevent them from making major gains a year later.
I imagine voters will shrug off impeachment similarly in 2020.
Right now, the polling is less conclusively against Democrats than 2013 polling was against Republicans. Trump’s approval rating has barely budged during the impeachment process, seeing neither the cratering in support that Richard Nixon saw during the Watergate investigations or the surge in support that Clinton saw during his impeachment. The country is largely divided on impeachment, as they are on Trump. Even if polling indicates impeachment is less popular in swing states, just because a given voter says in a poll taken in Dec. 2019 that he opposes removing Trump through impeachment, doesn’t mean that person will vote for Trump next November or base his Congressional vote on the impeachment issue.
Given the velocity of political news in the Trump era, my best guess is the impeachment saga will be folded into people’s overall impressions about Trump and will be supplanted by hundreds of controversies of various degrees of significance in the next 11-ish months. In the end, it will have very little effect on the outcome of the election.