The problem is that the American people have a memory of about 4 days, and the next election is
about 380 days away.
The only way to have a lasting outcome of this thing is to make sure the GOP pays such a heavy price that they never try this stunt again in the rest of Obama's Presidency. If they decide that they can't use either a government shutdown or a game of chicken on the debt ceiling to force negotiations, then they will have to work in the normal way the democracy is supposed to work. If the learn that hostage tactics don't work, then they will have to work within the system, and in that system, Dems control the WH and the Senate, so the GOP should not expect to get very much of what they want.
So Obama must hold the line. And he can easily do that as long as the polls keep showing this is hurting the GOP. It is unfortunate that many people will be hurt in the short term, but that is still a lot better than capitulating and allowing the terrorists to take hostages again in a few weeks. So I don't think this is going to be finished for another week. The GOP is in the process of crumbling on this issue. We have to let them crumble the rest of the way so that there won't be a single respectable Republican who says "Gee, that almost worked. Let's try it again."