Well, I think this is what is clear about the Republicans' current behavior:
Their entire plan was to shut the government down and blame the whole thing on the Democrats. That's it- there was no more to it than that. You can see this in the way that, every time one of them got near a microphone, all they have wanted to do for weeks was to claim that the shutdown was all the Democrats' fault. But they ran into a slight hitch. They counted on the compliant mainstream press to carry water for them, and by and large the press came through. The problem was that this time around, their fairy tales were so utterly preposterous that they haven't been able to sell people on them.
Well, now they are facing an economic apocalypse, and they are such a belligerent, hostile bunch of people that they can't find a way to walk back from the edge of the cliff. So, what is going to be their strategy if they do send the world economy into chaos? I believe they have two tricks up their sleeves. First of all, they are going to try to back Obama into a corner, where he has to take whatever action he can to prevent a catastrophe from taking place, and then they are going to impeach him for exceeding his powers, no matter what he does. Second, when there is not enough money to pay our debts, they are going to try to force Obama to prioritize payments to our "creditors," i.e. corporations and nations that have boughgt our bonds, at the expense of Social Security and Medicare recipients. They are going to try to force the government to either dip into the Social Security trust fund to cover these payments, at which point they will scream that Social Security needs to be destroyed because it is running out of money, or they will try to see to it that Social Security recipients are just stiffed.
In either case, they are betting that they can generate an overwhelming sense of rage in the voting populace, which they believe they can manipulate to their own benefit. With an economy in shambles and a President in the process of being impeached, they are sure they can win big victories in 2014. And if they do succeed in taking back control of the Senate in 2014, they will actually be able to remove Obama and Biden from office.
Then the fun begins. Boehner already is barely clinging to his position as speaker of the house, the next in line to be President. As the removal of Obama grows closer, you can expect to see a scene among the likes of Ted Cruz, Paul Ryan, Eric Cantor, et. al. like something out of medieval Florence- a vicious fight to the death over who will be speaker on the day that Obama is driven from office. The person who emerges on top in that struggle is going to be as far from a democratically elected leader as Pol Pot or Idi Amin, and believe me, he will act accordingly.
Will it happen? Well, I think the Republicans are vastly overestimating the support they have for this sort of behavior, as can be seen in such things as their million man marches that draw 200 people. I don't believe they can win this game, but they can incite some real ugliness before they go down.
Update: So, Louie Gohmert said today that if Congress allowed the government to go into default, that in itself would be a reason to impeach Obama, even if he does nothing. So, they are getting ready to pull the trigger on impeachment, whether Obama does anything at all.
Get it over with, already, you sons of bitches. We know that's what you want to do. Do your worst, and then we can line you all up against a wall and shoot you down for the traitors you are.