The problem with most of these efforts is they haven't read the Bill closely. It is indeed unconstitutional, but mainly for other reasons, reasons that apply equally to Medicare, Medicaid, Social Security, and the "Income Tax" on compensation for labor.
Let's examine what the language of the statute says:
“‘(2) INCLUSION WITH RETURN.—Any penalty imposed by this section with respect to any month shall be included with a taxpayer’s return under chapter 1 for the taxable year which includes such month.”
“(2) SPECIAL RULES.—Notwithstanding any other provision of law—
(A) WAIVER OF CRIMINAL PENALTIES.—In the case of any failure by a taxpayer to timely pay any penalty imposed by this section, such taxpayer shall not be subject to any criminal prosecution or penalty with respect to such failure.
(B) LIMITATIONS ON LIENS AND LEVIES.— The Secretary shall not—(i) file notice of lien with respect to any property of a taxpayer by reason of any failure to pay the penalty imposed by this section, or (ii) levy on any such property with respect to such failure.’’
--seems exclude characterizing it as a fine, but only a tax on self-insuring.
Consider those words carefully, and how they could or would be applied, and how the tax might be avoided.
It is a longstanding principle of law that if there is no penalty for noncompliance with a law, it is a nullity, merely aspirational or rhetorical.
The above words essentially mean the only way the IRS could collect would be by withholding money from a refund or benefit. But there is no withholding for true income, as from rents, interest, dividends, or capital gains, and one can reduce the withholding from compensation for labor by adjusting the number of exemptions claimed on one's W-4 form, or checking no withholding, leaving one to pay a "tax" at the end of the year, but leaving the IRS no way to collect the penalty for not purchasing health insurance. Even if the IRS takes one to court and gets a judgment, such judgment will be effectively unenforceable under the above language.
In other words, the proponents of the Bill were so concerned about avoiding grounds for a constitutional challenge that they gutted their own bill, making the entire scheme fiscally untenable, as though it weren't untenable enough already.
I see this leading to many good jokes on the late night talk and comedy shows.
However, it will also be a joke on the above mentioned efforts by state AGs and legislatures, who may offer some political theater but no legal results, and probably look silly in the process. Their efforts are misconceived. What might work is my proposed Nullification Commission in each state. See http://constitution.org/reform/us/tx/nullification/nullcomm.htm . Lawsuits and state legislative resolutions won't work. Indeed, they are likely to make the situation even worse when they fail. This undertaking requires more strategic subtlety than has been exhibited so far.