Of course Congress could simply remove the ability for the federal courts to hear such cases but for some reason, no one has proposed it.
In a balancing of the harms analysis, (something the courts do regularly) the harm done to us by Congress trying to enforce such an ill-advised Act would be much greater than the perceived potential harm by the application of the Full Faith & Credit mandate to these marriages.
The vast majority of the public simply doesn't give a tinker's damn about them. In fact, it wouldn't be unreasonable to predict that ten years from now the furor won't even rate a footnote in the history of the opening years of this century. It will be as non-eventful as the former state statutes prohibiting interracial marriages.
Is it merely rhetorical to ask: What if Congress had been persuaded by Southerners in the 1960s to forbid the federal courts from taking jurisdiction of cases on state statutes forbidding interracial marriages or desegregation in public faciliities or in interstate commerce? Yes, it is rhetorical, such an attempt would have failed miserably---and properly so.