Either side could give into the other, or propose a compromise, or something, but both are holding a hard line and letting the government shutdown.

Now, I suppose you could argue that one side or the other is being unreasonable, and that it's impossible for the "reasonable" side to reason with the "unreasonable" side, but then you'd have to argue which side is reasonable, and I tend to think that they're both being unreasonable. On the democrats side, they did ram through a highly controversial agenda (Obama Care) while they had a brief window of power, and they're not willing to compromise on that. On the republican side, they are trying to bully the democrats into giving up on Obama Care when they can't remove it by voting it out.

I'm not going to claim to be an expert here, and from the media that I tend to listen to, it does seem like most people think the republicans are more to blame, but I'm pretty sure if I listened exclusively to Fox News or something, then I'd have the opposite point of view. Even listening primarily to more liberal media (NPR and Comedy Central are probably my biggest news sources), I have yet to hear anything that would really convince me that the republicans are at fault, and if I haven't heard it, I think it's reasonable to assume that such an argument doesn't exist.