You like to think that, but in actual fact the good major is questioning his orders, not the Constitution. He says he won't follow orders, unless a court rules that Obama is authorized to give them. It's a very cute point... but it is not the military's job to make it.
There was a reason our founders wanted the president to be a natural born citizen.
The Founders were also well aware of the dangers of a military whose power and control lay outside the control of the civilian leadership. Indeed, civilian control is the founding principle of the US military.
One implication of this lawsuit is the assumption that the military (not just this one soldier) has a right to question its orders in this manner. In a very real sense it places the military somewhat outside the control of its civilian leadership.