The main leverage the IRS will have is the refund “offset.” That simply means if a taxpayer is due a refund, but has also incurred an Obamacare penalty, the penalty will be subtracted from the refund. So a taxpayer who has a $500 refund coming but incurs a $695 Obamacare penalty will receive no refund.

In addition, that taxpayer might face a letter and a phone call — or a series of them — from the IRS telling him to pay the rest. Anyone who has received a letter or phone call from the IRS knows the experience can be quite intimidating. Or, in the words of the administration’s Supreme Court brief: “Offsets, correspondence, and phone calls are consistently some of the most productive tools in the federal tax collection process.”

Will the government really do that? The answer is not clear, or at least not publicly clear. (In response to inquiries, IRS officials sent boilerplate, non-enlightening clips from IRS publications.) But the administration’s level of aggressiveness will likely be determined by how many Americans voluntarily comply with the law.