Indeed, prior shutdowns haven’t had long-term electoral implications. Republicans recovered on the generic ballot by February 1996, just a month after the final shutdown of that period ended. And in the elections later that year, they held onto their majorities in both the House and Senate. Clinton, meanwhile, recovered his lost support by March 1996. He would go on to easily win reelection later in 1996.
Basically, America put the same people who shut the government down back in office.
The 2013 shutdown tells the same story. Despite losing the shutdown blame game, Republicans jumped to a lead on the generic ballot by late November 2013 — their first of the year. In the 2014 midterms, they expanded their majority in the House and won back the Senate. Meanwhile, Obama continued a long-term decline in his approval ratings in the months following the 2013 shutdown, but recovered to his pre-shutdown approval level by April 2014.