Backing down on a government level just isn't going to happen. They've got their apology from the newspaper, and that's all they're gonna get. And if they think burning embassies makes it more likely for us to back down, well, think again. The truth is, there's nothing they can do that will truely put us under pressure.
1) We're a net exporter of oil and natural gas. Nothing to come for there, if they thought they might be able to squeeze us.
2) Most of our major trade partners are in the western world. They're not going to boycott us, even though some have demonstrated less support for a loyal ally during this than one might have hoped.
3) Terrorism? Our total land border is less than 100km, and that's with Germany. It's not as easy to sneak in as they might think. and unlike many countries, aquiring weapons once in-country instead of smuggling them in is not a simple task here. Besides, terrorism will just make it even less likely for us to back down, just as the burning of embassies has done.
Basically, the ball is in their court. Back here, everything is going just fine, and to most of the muslims who live here the matter is considered settled.