current GOP plan looks to be a short-term debt-limit increase while keeping the government shut down.
Right. Let's see what the problem with that is, hm?
The shutdown is really quite unpopular and the general public seems to have little illusion about who actually is to blame for it. More people than not now understand that not raising the debt ceiling would be a very bad idea. Therefore, the best thing they can think to do at the minute is prolong the shutdown, and remind people after a matter of weeks that they are very irresponsible regarding the credit of the US government.
I don't think we can call this a strategy regarding either policy or politics. They aren't getting what they want in any event, and they will look very bad while not getting what they want.
I'm not cynical enough to say that this is a good thing for Dems or that they won't think of something to do that's somehow worse before the 2014 elections. I'm not even in the horserace #winning mood. But if this is a sign of where the collective GOP head is at, I will conjecture that it is very dark there.