Goodridge does not establish permanent martial law or declare the Commonwealth a monarchy; and it cannot plausibly be argued that every disagreement about allocation of power within a state government--even a very important disagreement--raises a question under article IV, § 4.
The claim here is that judicial activism brings into being a de facto kritarchy--"rule by judges."
The problem is that, if a Federal court overturns the Supreme Court of Massachusetts on these grounds, it would implicitly call into question Federal judical activism, as well.
In my opinion, neither the appeals court, nor SCOTUS, will want to open this can of worms.
My answer to that question is this: The people who oppose gay marriage know that the imminent "sky is falling" tone of their pleadings is the best thing they've got going for them. Upon careful deliberation, the Federal court system will leave Massachusetts law alone, and leave it to the people of that state to deal with the issue in their Constitution. In fact, the very prescence of a Constitutional Amendment to change gay marriage into civil union shows that the process is working, and that there is no need for the Federal courts to interfere in it.