The "shutdown" would only happen if either the Senate couldn't pass the budget when they get it it (or it gets tangled up in conference) or the bill hit the President's desk and he vetoed it. Either way it's on the Dems if that happens. The House has already passed the budget.
But that was the same situation in 1995. Clinton vetoed the budget, but with help from Gingrich, he was able to spin it as a Republican thing, successfully. It knocked the wind out of the Republican house. Some things are the same as then. Like the fawning press that will play the shutdown however the administration wants, like they did in 1995. Of course, in 1995 there wasn't much choice to Big Media. This time around, there is. People have more options than what the establishment wants you to hear so the public may not go along the same way that they did in 95.
The Tucson shooting? 15 years ago the polls would have reflected the media spin that it was a Tea Party-Palin hit job. Instead the polls showed that people just didn't buy it.
So if the administration thinks that going for the shut down is a sure thing to help them... well, I don't think it's a sure thing this time.