This is whats really going on, as succinctly as possible:

“Obamacare continues to be our No. 1 fundraising tool,” said Andrea Bozek, communications director for the NRCC. “We have broken records in our online fundraising and engagement in the last few weeks. Thirteen months is a long time in American politics, and it’s going to seem even longer for House Democrats who will be spending that time defending Obamacare’s broken promises.”

Basically, a lot of money is pouring in to Republicans from constituents who are hearing Obamacare and are seeing a fight against Obama, who is the epitome of evil. The NRCC is pulling on the slot machine arm and money keeps pouring out. They will keep pulling on the slot machine all the way till the deadline, because money will keep pouring out, and there is no reason to stop collecting it.

They figure in 13 months no one will remember this Government shutdown. If there is some sort of permanent economic consequence, people might remember that in 13 months, so its likely that they have the presence of mind to give in right before the last moment so that doesn't happen. But there is no way that they are going to do so beforehand because the controversy is causing gold to literally rain from the sky, and they don't have to give any of these donations back once they capitulate.

Republicans will continue to attempt to associate any Healthcare related problem or annoyance with Obama and the Democrats. Any hiccup or issue at all with the implementation of this system will be responded to with the refrain: "Oh, if only it wasn't for Obamacare!" This is simply because it is strategic to do so. People are more likely to notice minor things that are annoying to them whereas they aren't keeping track of who does and does not have access to healthcare unless they are a member of the minority of people who does not have access now.

This will continue unless one of two things happens:

1. People remember these shenanigans at the polls, and the consequences cost the Republicans in a way that is more important than the funds they are raising.

2. Obamacare gets implemented, people become accustomed to it, they decide its no big deal and stop giving the Republicans money whenever they bitch about it. (See Medicare.)