I don't know enough about how health care works to really weigh in substantively on this ue, but a brief reading of the resource material provided leaves me quite skeptical.
For one, it's the heritage foundation and they're notoriously conservative so they're constantly looking for ways to take potshots at the president. Secondly, Ed Haislmaier, the guy who's numbers and stuff they cite in the article (who by the way is employed by them) as evidence to back up their claim isn't a statistician, he's not a scientific, he's not a research fellow at a non-partisan institution: he's got a bachelor's degree in history and a record of conservative analysis.
Not exactly the most reliable source; that doesn't mean this couldn't happen, but I'm not holding my breath on this one until I see the information corroborated by an actually trustworthy organization.
I also find it funny that the article in which the New York Times discusses the issue only has information from the Heritage Foundation to cite as well. It's like the Heritage Foundation is linking to analysis of their own opinions in order to support those opinions -- seriously circular logic. I have to wonder if they're conjuring up this entire possibility for cheap political points.