Most economists would say there is conceptually no difference between a coffee shop (a) charging 5 cents more for each drink and giving a 5 cent discount to people who bring their own mugs and (b) charging 5 cents more to people who don’t bring their own mug. The price you pay for a drink is the same in each situation (both when you have your mug and when you don’t).
However, to some people the distinction is a big deal. Most grocery stores give customers discounts for bringing their own bags, but protest against proposed requirements to charge for each plastic bag. Apparently, judges, lawyers and much of the US population also don’t agree that the two situations are equivalent. The mandate to buy insurance has led over half the US States to challenge its constitutionality. But is that requirement really that different from some other incentives that US citizens have faced for decades?
The way the Obama administration chose to write the law is as follows. Everyone is “required” to buy insurance. But clearly, the government cannot truly force people to buy it or impose severe punishments. Thus, the “price” for not buying insurance is a tax penalty. By now, it should be clear that the Obama administration could have gone a different route. Instead of imposing a tax penalty and calling it a “mandate”, it could have simply raised taxes and introduced a tax deduction for people who buy health insurance. Same exact incentives, much less legal trouble. We don’t call the mortgage interest deduction a “mandate to buy a house” and we don’t call the deduction for dependents a “mandate to have a child”. No one has sued over them (at least that I know of). But changing something from a reward to a penalty is apparently enough to land you in the Supreme Court.
Maybe the Obama administration knew that people would react to the other framing differently? Although I don’t know of any studies that show this, people appear to dislike explicitly paying more for not doing something, like not bringing their own mug or grocery bag and not buying health care (even though you are implicitly paying more when you forget that mug). This would imply that people are much more sensitive to tax “penalties” than to tax “deductions”. I’m guessing that calling something “mandatory” and penalizing non-compliers has larger effects on take-up than simply providing a tax deduction for doing something.
Of course, it’s also possible that a proposal which raised taxes and introduced tax deductions for buying health insurance would have never passed Congress (or that the administration never imagined so many states would challenge the law).