I am not positive that it will give the Democrats the house, but I think that people will remember it. A forced shutdown for no logical reason is not in the best interest of the country. It was pretty clear to many that it was just a political stunt and a pale attempt to harm Obamacare. Something that went on as planned (although with many website issues) anyway.
As I see it, and many other people are seeing things, the government shutdown was the fault of the Democrats and not the Republicans. This country is slowly but surely opening their eyes to the fact that the Democrats are turning the United States into a place of control and almost Communist place, which was proven by the shutdown!