Some other provisions of the reform package aren't separable. For example, Congress can't tell insurers they have to cover pre-existing conditions unless there is an individual requirement (or mandate) to buy insurance. Otherwise, people would rationally not buy coverage until they get sick, and the whole insurance system would break down.It's more problematic than this. In order to mandate health insurance, Congress must endow some administrative body with the ability to decide what exactly qualifies as "health insurance." If private insurers decide to offer coverage beyond the minimum required to qualify, they'll be saddled by customers with preexisting conditions (who they are no longer allowed to deny) seeking to take advantage of the superior coverage. This is untenable, and there is almost surely no stable equilibrium other than providing the minimum.
The effects are profound. Under this system, the economics of adverse selection imply that the level of coverage will effectively be determined by government fiat. I am not sure that this is bad; the benefits from universal care may outweigh the loss of competition and variety in the marketplace. It will represent, however, a massive shift toward government control in health care. And it means that progressives cannot respond to complaints about rationing by saying "well, you can always buy extra coverage on the private market." When a law banning discrimination against customers with preexisting conditions effectively prevents insurers from offering any extra care, this is simply not true.