Whether or not the House passes a plan is irrelevant. If it passes, it will die in the Senate. The Senate will then pass a bill, that will die in the house.
We are going into "default", boys and girls.
But not really.
To go into default, we'd have to stop paying the interest on the debt. I don't believe Obama will do that. On 3 August, Obama will announce that he will continue to service the debt, to prevent economic collapse world-wide, and fund Medicaid if we can afford to, because those on Medicaid are poor by definition, and will likely die without. I believe he will also say that social security checks won't be going out, at least not all at once. To keep from being blamed for that, He'll have to say that he didn't have a choice. The republicans in congress forced his hand.
I think that there would be a firestorm of protest. There are probably a lot people who voted for tea party congressmen who won't be getting their guvmt checks.
I've considered the 14th amendment, but I don't think Obama will invoke it. For one thing, it would refocus attention away from Congress to the President, and he would want the focus on the Congress. The other is, the 14th pretty clearly has to do with the Civil War, and I don't think the current SCOTUS will back Obama's interpretation.
So, on 3 August, we enter the next stage of this game of chicken: "default".