In order for Alexander's comparison to make sense, here's what would have happened: imagine Obama asked Congress to approve the Affordable Care Act, but instead, Congress did the opposite, approving a measure ordering the president not to change the existing the health care system. Obama, undaunted, sold weapons to North Korea and then used the profits to do the opposite of what Congress instructed.That sounds about right.
Benen's whole post is good, but I'll expand some of the history, anyway. He notes that there's plenty of precedent for public-private partnerships in these kinds of cases. Alexander's point is that if Congress doesn't fund it, the government can't pay for it. That's correct -- but that's not relevant here, since what HHS is doing is finding funds for a private entity ("Enroll America"), not a government agency. Alexander thinks that doesn't matter because the Contras were also a private agency, but the major difference is that in the 1980s the Boland Amendment and other law specifically prohibited the government from doing anything to help the Contras; the narrower issue of Iran-Contra was whether that prohibition applied to National Security Council staff. In this case, while Congress didn't supply any money for HHS to fund Enroll America, they did not specifically tell HHS that it couldn't implement the law as part of their normal responsibilities.
At any rate, Alexander has forgotten even more: the larger problem of Iran-Contra wasn't that the administration was raising private funds for the Contras; it was that the Reagan Administration retailed weapons to Iran and then used the profits elsewhere. That's not the executive raising money from the private sector for something in the private sector; that's the executive generating new funds that they control and that Congress can't touch. Indeed, the real scary part of Iran-Contra (and here, I'm working from memory) was the idea that this could be self-sustaining; the executive branch could develop permanent funding streams that Congress would have nothing to do with. That would indeed upset the Constitutional balance, and that's probably the core of why Iran-Contra was such a large scandal.
And back to Benen's point: unlike the Contra war, which Congress opposed and was trying to stop, the ACA is actually law; it's the responsibility of HHS to attempt to carry it out as best it can. Certainly, if there's no funding for a specific task, they can't spend money on it. But there's no Congressional prohibition against trying to execute this particular law; indeed, the presumption is exactly the opposite, that HHS has been told by Congress to enact Obamacase as best as it can.
And meanwhile: Nice catch!