I'm pretty confident that only the parts that were in the case, in this instance, requiring the purchase of health care, would be ruled unconstitutional. This happened with parts of the patriot act. However, I also believe that the law in question is what matter, like the text could say that once part is null and void, so is the rest. I know that parts of the New Deal was ruled unconstitutional leading to quite a stir, court-packing, etc.
The most interesting thing here really is how its argued once it gets to the supreme court, and what the justices choose to see. I could see them saying that for there to be a mandate, there has to be a public option available. the 10th amendment argument is shaky at best seeing a lot of the federal government would fail that test, its a can of worms no one wants to open.