There is no "could". If the exec branch orders the US military to fire on demonstrators, there will be tanks in DC arresting the executive AND legislative branches wholesale. Oath is to upholding the constitution, not tyrants elected with a slick campaign that fooled millions.
How about a different scenario,
where a state refuses to enforce, or allow to be enforced,
an unconstitutional law within the boundaries of that state,
0bama sends out fedthugs, and the people of the state arrest said fedthugs....
now what?
But what if the executive branch wanted it to look like you and the rest of the people in your ‘compound’ burnt themselves to death?
Obama doesn’t need to command the US military to do anything. He just needs the ATF.