You have a shallow understanding of our justice system and I can explain why...

You say:  "Why not support the president issuing an EO declaring martial law and rescinding all Americans' rights until someone can win in court?"

Your answer is actually the answer Trump got when he tried repeatedly to do his ban from 6-7 Muslim majority countries. One of these executive orders was literally stopped by injunctions before they could be implemented.  Because Obama is a constitutional lawyer he knows which actions he can take that (at a minimum) will not warrant the use of an injunction.  That is what makes him competent regarding constitutional law that he never did in 8 years what Trump managed in his first month (get an injunction that stops an EO before implementation).