I haven't seen details yet, but it seems to me there are two ways to go with this.
Option 1: "We can't be at fault; we passed the Government Shutdown Prevention Act."
If you're going that way, then you really, really need a provision that explicitly says that Democrats in the Senate are to blame for the shutdown. Then you can go on Fox News or whatever and explain that everyone agrees that the Democrats are to blame; after all, just look at the bill that says so!
But that, I think everyone will agree, is lacking in firepower. No, what they really need is:
Option 2: "The Democrats don't agree with our Shutdown is Bad bill -- so they're for a shutdown."
In that case, might as well add provisions that say that we Support the Troops, and that America is an Exceptional Nation, and that Gosh We All Do Love the Flag, and that Kicking Puppies is Bad. See, if they don't pass this (and H.R.1), then Democrats oppose all those things!
The really scary thing, of course, is that it's possible that the Republicans actually believe that this kind of obvious, boring spin could affect anyone who wasn't already completely convinced of the GOP cause. Believing your own spin is dangerous, but so is believing that you can spin anything.