Watching the events unfold in the campaign, I have had cause to recollect that the Supreme Court has already ruled in Cousins v. Wigoda, 419 U.S. 477 (1975), and Democratic Party of U.S. v. Wisconsin ex rel. La Follette, 450 U.S. 107 (1981), that the Illinois state courts got it wrong "in according primacy to state law over the National Political Party's rules in the determination of the qualifications and eligibility of delegates to the Party's National Convention" with respect to the dispute over the seating of the Illinois delegation to the Democratic National Convention and, with respect to the Wisconsin delegation to the 1980 Democratic National Convention, that Wisconsin could not "compel the National Party to seat a delegation chosen in a way that violates the rules of the Party."
The Cousins v. Wigoda case is another of which some tales are told in John Tucker's book, Trial and Error: The Education of a Courtroom Lawyer, one of my favorites.
So, on the face of things, there is no constitutional impediment to the enforcement by the National Committee of its rules against Michigan or Florida for conducting their primaries too early - which must be why there have been no lawsuits before now. I note that at least in the Illinois case, the impression I get is that the litigants filed the case before tame state court judges to get their injunction, and the federal courts had no role until the cases wert all the way through the state appeals courts.