If the Mandate Is a Penalty and Not a Tax, Then Let's Codify the Distinction

So if the White House is going to continue to insist that the mandate is not a tax but a penalty, despite the Supreme Court's ruling that the mandate is only constitutionally viable as a tax, then how about we resolve this issue formally, and settle things once and for all? Writing at The Volokh Conspiracy, David Bernstein has a clever idea for how that might be accomplished:

I'd schedule a new vote in the House on the individual mandate, but replace the "penalty language" with language specifically acknowledging that the "penalty" is actually a tax. If the Democrats vote "aye," they've acknowledged breaking the Obama pledge not to raise taxes on the middle class. If the Democrats–specifically those who already voted for the mandate–vote "nay", what becomes of the tax argument in future litigation? Seems to me that Roberts was only able to argue that the mandate is a tax because no one [officially, by Congressional vote] specifically said it wasn't. At least it would look very peculiar that the Court upheld the law on a theory that Congressional supporters of the law refuse to adopt.

If the White House is so certain that the mandate is not a tax but a penalty, then administration officials shouldn't mind other Democrats saying so formally and codifying this distinction into the law.