Before the shutdown occurred, there were concerns that it would hurt Republicans. And while recent generic house polls show Democrats with a slight lead since the shutdown started, it's not as bad for the GOP as feared. While the last government shutdown occurred when I was still in diapers, the worst thing that happened for the GOP is that they lost a net of 3 house seats. They actually picked up a net of 2 in the senate which take that into account percentage wise, their margin increased overall. In the 104th Congress, they held I believe 230 house seats and 53 senate seats. At the start of the 105th, they held 227 in the house and 55 in the Senate. Figure out those numbers for yourself.
Interestingly enough today, Sabato's Crystal Ball released a column in which they said it'll be moderate Republicans in districts that voted for Obama paying the price for a government. Very much the same way moderate Democrats who were in districts that voted for McCain and Romney did for Obamacare. I very much respect and admire the insight they bring and it's possible for this scenario to happen if something badly backfires, but the 2 situations aren't comparable necessarily. Like I said before while polls suggest public blames GOP for government shutdown, Obama and Democrats don't escape this situation either. As I am writing this, Real Clear Politics average shows a negative 7 point in Obama's job approval.
Also there's the fact that every poll I've seen shows the public doesn't like Obamacare by a majority margin (some by as much as 20 points). To their credit, they do account for the albatross Obamacare still is for Democrats. Ultimately regardless of whether you thought it a good or bad idea to use a government shutdown to stop Obamacare, the GOP now has no choice but to drag this out. Also worth mentioning back in the last shutdowns, Clinton kept constant communication open with Newt and the gang and signed bills keeping sectors of government open. Here Obama and Reid are purposefully refusing to take up bills to keep the national parks open and closing the WWII memorial down just to humiliate the GOP. Keep passing bills to keep as much of the government open as possible and expose Reid and Obama for the lying bastards they are.