If you really want to be both more accurate and more true to your critiques, try something like "ExpensiveCare" or "ConstrainedSupplyCare" or "BubbleDemandCare" or something like that. I could even see critics attempting something like "UnfairCare", referencing the fact that young healthy people with incomes are now paying for old/unhealthy/indigent people's healthcare in addition to their own.
But "Obamacare" is silly, non-descriptive, purely partisan, and universally detracts from any conversation about it.