This not a question of the Constitution. It's a question of statutory interpretation.
By the time it gets to the Supreme court it's matter of politics, intent, clarity and outcome as much as statute. I don't know enough about US politics to know whether the Supreme Court would strip hundreds of thousands of Americans of their healthcare on a technicality, but I suspect not. And robbing the law of any effect due to the way it was worded seems equally unlikely unless it was based on a Constitutional Principle, because it would put the Supreme Court in the position of overruling the will of both legislature and executive simultaneously. Absent of some constitutional principle, it seems more likely you'll end up with mandatory exchanges.
To be honest I'm finding this whole discussion hard to fathom. Interpreting laws is difficult, and they can often seem contradictory unless you're used to them. I just find it hard to move from that to the idea that the Supreme court would torpedo the US healthcare system over poor wording, just to please the political enemies of the president. Is that really how it works over there? Because poorly worded laws are not exactly unusual...