Btu I bet they blamed the last shutdown entirely on Republicans just as much in the media that people did see. Which is often considered a key factor in the 1996 election results (where not only Clinton won but to my understanding more than a few Republicans got destroyed in the elections).
I truly think the 1996 election was won by Clinton because the economy was working well at that point and the GOP decided to run Bob Dole as the presidential candidate and who was no where near a match for Clinton.