Not only did the U.S. Congress have the authority to intervened, they did intervene. But, the best forum for intervention was at the legislative branch of the state of Florida. When Florida failed to do the right thing, that should have been it. But, the GOP intervened, as awkwardly as it could, and tried to make the SCOTUS take the case.
Separation of powers does mean something and should be respected. I'm sure that you'll write me back and point out the errors in my thinking or my recollection of the fact, or perhaps, both.
The Florida legislature did intervene, but they were overturned by the Flordia Courts.