(1) Is it that voters will punish the party that does the shutting down? (2) Or, is it that if you are perceived to be fighting for the electorate your party will be rewarded? Help me out here, I've had only six years of post graduate study.
The reality is the second, but the friends the politicians listen to on the cocktail party circuit will push the first. The GOP typically takes the wrong lesson, in this case, "Voters will punish the party that does the shutting down." Because of the media, as it's constituted today, that party is
always the elephant. It doesn't matter who's fault it really is. They blamed Reagan when he was President, and they blamed Gingrich (and later Cruz) when they're in Congress.
No wonder Republicans are gun-shy about it, they always get blamed no matter what.