This is, to be sure, a real overlap. It might even be a fundamental similarity in a context where the plausible alternative was a single payer or nationalized model.
But thats obviously not the plausible alternative a statute that eliminated the American health insurance industry while steeply cutting the compensation of most medical professionals would (with the exception-that-proves-the-rule of abolishing slavery) be unprecedented in American history, and would also have no precedent in any high-veto-point system. (Even in the highly centralized Westminster systems of Canada and the U.K., in a context where comprehensive health care reform was a lot cheaper, the doctor lobby very nearly derailed universal health care and had to be bought off.)
And in 2009, the idea that single payer was a viable possibility to 60 votes in the Senate requires ingesting enough hallucinogenics that youd better have good insurance already. So, in the relevant context, the presence of a mandate in the ACA doesnt establish any kind of fundamental similarity with the Heritage Plan. It just means that its universal health care reform designed by a non-moron.
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And even though the Heritage Plan was just a decoy, its still eminently fair to observe that nobody noticed that the mandate was the greatest threat to human freedom ever when it spent years as the nominal Republican alternative.
Theres another variant, made by various people up to and including Obama itself, that notes the mandate in the Heritage plan to rebut charges that the ACA was volume 2 of the Communist Manifesto. Which, OK I guess, but I dont endorse this line of argument, among other things because it gives Republicans too much credit and because it does begin to imply a substantive similarity between the programs even if it isnt intended.
Which brings us to the the most important dissimilarities between the plans:
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Perhaps recognizing how feeble the argument is, the commenters trying to maintain the lie generally move to a bait-and-switch when they say the ACA and Romneycare the plan passed by massive supermajorities of Masschusetts Democrats over Mitt Romneys many vetoes are just the Republican Heritage Foundation plan, they also mean that its like the plan that John Chafee introduced in 1993 as an decoy alternative to Clintons health care reform proposal. While not as nearly progressive as the ACA most importantly, it replaces the Medicaid expansion with medical malpractice reform it is more like the ACA than the Heritage Plan. But the comparison remains transparently silly. First of all, it was of course never the Republican alternative, as no non-trivial number of Republicans have ever wanted to enact it (cf. every Republican-controlled house of Congress since 1994 passim.)
And second, citing John Chafee who was far to the left of the typical Republican in 1993 as representing Republican health care policy preferences is an act of monumental bad faith, like citing David Souter as the typical Republican judicial appointment or George Wallace as having the typical civil rights policy preferences of a Great Society Democrat.
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Lets say the a liberal think tank developed a proposal identical to the ACA, and Bill Clinton used the power of the bully pulpit to ram in right down Congresss throat in 1993. Barack Obama takes office in 2009 and proposes changing ClintonCare by making employee heath insurance benefits fully taxable, repealing the regulations requiring insurers to cover anything but catastrophic care, throwing many millions of people off Medicaid and devolving it further to the states, and enacting Paul Ryans proposal to end Medicare.
Would any of the nominally left critics of the ACA be saying that Obamas proposed changes were no big deal because theyre fundamentally just a minor variation on the Democratic, Liberal Think Tank X plan? Of course not they would be leading riots against the greatest domestic betrayal by any Democratic president in at least a century, and theyd be right. Nobody really thinks that the Hertiage plan and the ACA are meaningfully similar. Its just that some people refuse to compare the ACA to the status quo ante rather than a superior alternative that had no chance of passing, and
saying that Obama just signed the Heritage Plan sounds a lot better than being open that your offer to the uninsured and working poor until Congress can pass the Magic Ponies and Unicorns Act of 4545 is the same as the Republican one: nothing.