Citizens United isn’t directly on point. That was a question of positive corporate speech while this law, if it’s struck down will be struck down under the corporate compelled speech doctrine. But they are both part of the same body of Constitutional law that the federal courts very much have jurisdiction to enforce.
That's unlikely, as such an argument is a complete non-starter.
If I were arguing against the law, I suspect (shooting from the hip without researching it) that the most fruitful line of reasoning would be that the federal government has preempted the field of interstate communications transmission by a combination of the FCC's organic statute and the CDA. This is a better argument because, despite what some on HN believe, there is a half-century of Supreme Court precedent that compelled hosting is not compelled speech, and because of the doctrine of constitutional avoidance.
As an interesting aside, Justice Kagan had some involvement in one of the issues underlying one of the cornerstone cases in this area. Though she was not a party and does not appear to have been among the amici, when she was Dean of Harvard Law School she opposed military recruiting on campus due to the Don't Ask, Don't Tell policy. The Solomon Amendment required non-discrimination in hosting speakers for recruiting purposes, under threat of the loss of federal funding. That compelled hosting was challenged and upheld in Rumsfeld v. FAIR, 390 F. 3d 219 (2006).
I ask because there are so many examples of compelled speech that have not been struck down. Witnesses are required to testify. Various companies are required to print warning labels, nutrition facts, country of origin, and such on their products. Politicians are required to say "I approve this message" in advertisements. Doctors and pharmaceutical companies are required to describe side effects of medications. Police are required to give Miranda warnings. Professors at many state universities are required to add a few paragraphs of mandatory text to their syllabi, including a notice that they are mandatory reporters who are compelled to tell the government what they know about certain events.
It's so common that I wonder (despite frequent claims in these discussions) whether a prohibition against compelled speech actually exists at all.
The Court tends to defer to history as a way of understanding how the framers viewed an issue so things like compelled testimony would likely be safe. My pet thought experiment is challenging the requirement to answer the census, particularly with it's much-expanded survey questions. Perhaps I can be compelled to say where I live and who lives with me, but can I be compelled to answer questions like whether any of us are gay?
"Because the First Amendment would not prevent Congress from directly imposing the ... access requirement, the statute does not place an unconstitutional condition on the receipt of federal funds." (emphasis added). Rumsfeld v. FAIR, 547 U.S. 47 (2006).*
I'm not sure where you're getting the argument that this is inapplicable, but it sounds like some of the talking points coming from the Internet outrage machine (e.g., the OP). I strongly encourage you to read the primary sources.
* This is the correct citation. The one I entered yesterday is no longer editable but refers to the Third Circuit case preceding the Supreme Court case; switching tabs on my phone is a little harder to keep track of than on my computer, and I apologize.
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