Mark Blumenthal thinks it's "too soon to anticipate how Americans will react to a government shut down, should it occur." What we do know:
[L]arge majorities of Americans want President Obama and the Republicans to reach a compromise and avert a shutdown. Four different surveys released in the last two months shows majorities ranging from 55 to 81 percent expressing a preference for compromise rather than a hard line leading to a government shutdown.
As the above chart from Pew shows, Republicans are more hostile towards compromise. But the key group, Independents, are closer to the Dems on this than the Republicans.
The Dish 