Back during the first modern government shutdown in 95/96, Republicans started by saying they were going to break Bill Clinton by shutting down the government. (This is actually why, aside from length, the 95/96 shutdowns became so iconic and toxic, despite the fact that a number of mini-shutdowns - aka 'spending gaps' - had occurred in the 70s and 80s.) But when that didn't work, they slowly turned to saying that Clinton was enjoying the government shutdown and finally that Clinton himself had actually shut down the government. By the late 90s it had become a staple of Republican thinking that the failure of the shutdown gambit was rooted in Clinton's ability to convince the media and thus the public that Republicans shut down the government rather than him.
House Republicans are now reduced to arguing that Obama's supposed cynicism in willingly letting the GOP swirl down the drain is bad news for the President. Other arms of the GOP express confidence that they're winning. Yet it's hard to reconcile that with the fact that they're furious with the people who dragged them into the fight.
What it all comes down to is that we have the same pattern: Republicans shut down the government and then go into a days or weeks run of testing out different arguments about why it's actually the president who shut the government down. And the urge intensifies as the public gets more and more upset. But the essential calculus remains the same. The Republicans forced a government shutdown. The public understands that. So intense unhappiness over the shutdown inevitably redounds on them.
To put it more succinctly, reality is a bitch.
As Jon Stewart so eloquently puts it, blaming the GOP for the shutdown takes you about as far out on a limb as blaming floods on water.
There are inflexible bounds to this spin war. The House GOP under pressure from the Tea Party shut the government down to force Obama's hand on Obamacare. The public opposes that by overwhelming margins (70%+). The public also blames the shutdown on House Republicans by a substantial though not overwhelming margins (the number who blame Obama, in the mid-30s, roughly matches the base of the GOP). No word games on the margins will change that. Not because the media is biased or Obama's a genius or everybody's out to get the GOP - just because that's what happened and people get it.