First things first. All presidents use executive orders. They are pretty much limited, by law, to the executive branch of government (i.e., the president can use them to give instructions to his Cabinet about how he wishes for them to do their jobs within their departments).
When a president runs his play around a bickering Congress to appeal to a disgusted American public, he knows all that.
He is not about to declare martial law. In fact, most of what he can do is only symbolic. But he hopes Congress will see his actions and follow him out of their deadlock.
For example, he can give an executive order to raise the salary of federal employees to $10.10 an hour but (whispering for emphasis . . .) most federal employees already make much more than that. So it is a symbolic gesture, a mere windowdressing, and the President knows that.
The discussion of whether the nation should raise its minimum wage to $10.10 an hour has already been analyzed in this space, so I will leave it for now.
Suffice it to say, martial law is not about to be declared. People who go to lengths to say the President will declare martial law only make themselves and their movements and their followers look really, really foolish.
They also show that they don’t understand the executive branch and the separation of powers.