A mandate for private insurance vs. a mandate for a single payer type system are two completely different things.
Another general issue that few are discussing is why anyone is confident that we're going to strongly enforce the new regulations on the private insurance industry and or that the industry won't find severe loopholes. And of course it's entirely possible that (as I've pointed out) when Republicans inevitably regain power (possibly directly because of this legislation in some ways) they'll exploit flaws in the system to further weaken regulations and gut the subsidies that mask inevitable price increases. And don't forget that it's not just about insurance premiums, it's also about co-pays, deductibles and drug costs. Just one loophole in one area can royally screw us.
Yes, I realize that technically that's possible with any reform, but it's specifically relevant in this case because the proposed reform is so damn weak and because it ultimately strengthens the private, for-profit system. That means it should be especially easy to take a mediocre system and make it downright horrifying in a relatively short period of time.
I know it's possible that might not happen, but of course the industry lobbyists are going to be fighting for that the DAY after the bill passes, especially with elections coming up.