Not entirely true. Every member of the military swears an allegiance to the Constitution, not to the president.
Not just every member of the military, but every member of the federal government, including all the "alphabet soup" police style agencies. Now, the question becomes, will such as those honor their given word, or not?
I know not what course others might take, but as for me, I choose to end my life as I've lived it, faithful to my G-d, loyal to the country I was born in, and true to my own given word...
the infowarrior