Funky idea, but I'm afraid it wouldn't work, for a number of reasons. First of all: drag. Most of what you need to get to orbit is speed -- 17,500 mph -- not altitude. In order for a balloon to provide lift -- and in order to harvest oxygen from the air -- you need to, by definition, be inside the atmosphere. And if you're inside the atmosphere *at all*, then you need to be as streamlined as possible. (If you look at any proposed airbreathing spaceplane, such as NASP, you'll see that it has a very un-balloon-like profile. There's a reason for this).

Even liquid hydrogen is so "fluffy" (with 1/11th the energy-density of Kerosene, for example), that tanks holding it must be relatively bulbous and drag-producing. This is why LH2 is actually an awful fuel for launching anything from the ground -- although it's great for upper stages, where drag isn't an issue.

The other problem is that a launch vehicle of even miniscule size would need thousands of pounds of hydrogen, and that the biggest balloon imaginable would contain, at best, a few hundred.

Cheers,

Nathan.