I actually think it will happen. When we were nearing the fiscal cliff, I thought that the GOP was just putting on a show for its constituents, showing that they would fight the evil Obama administration until the last minute before giving into reason. But then sequestration happened. With the shutdown, I thought, again, Republicans would put on their theater to satiate their base but ultimately cave before it happened. But again, the worst happened.
It's clearer than ever that the Tea Party is actually not playing a game that they'll abandon when push comes to shove, nor will they give into reason (much less know what the reasonable solution even is). They have their convictions, believe they're in the right no matter what, that Obama and the Democrats are in the wrong no matter what, and that - because the federal government is an evil institution that we're better off without - will allow any number of things to happen to get their way. Simply because they think they're David standing up to Goliath and because they frankly don't know any better.
So yeah, I totally expect the government to default, if only because many Republicans don't even know what that means.