Yes, if I were in receipt of orders from the National Command Authority and had properly verified them.
Don't hide behind "lawful orders"; do you have the courage?
Yes.
How would you verify the "order" was legit?
By verifying the emergency action message. To do so, I would use the procedures set forth to do so (Validate the EAM containing the firing order, entering the PAL release code, and turning my key).
How much time would you take before pushing the button?
As much as necessary to validate the order. Not very long at all, considering.
You are not a leader, just a follower....
To be a leader in a military force, you must first be a follower.
Armies, shorn of the need to follow duly constituted civil authority, turn into either agents of entropy, or agents of tyranny.
Which do you wish the American military to be?