I would absolutely take up arms or sacrifice my life to defend the Constitution.
Key word here is defense, BTW. The USA has spent hundreds of years fighting in places it shouldn't. It has helped but also seriously damaged many, many countries serving corrupt corporate and government (not constitutional) interests.
Given that not fighting, in this case, is to premeditatedly inflict the fight on someone else...
Who wouldn't stand their ground? Even an occupying force can be resisted, or have their occupation rendered so impractically expensive as to be infeasible.
Let the infirm, or those with dependents flee for safety. Let no good, able bodied man (or woman) yield his(or her) place in the world.
Why the hell fight for them? On top of that... what religion or atheists... say killing or violence is allowed?
Philosophically we should be post war now. The big guys cant touch the other big guys. Nobody has nuclear/bioweapons but they are willing to use them.
Lets just stop with the killing of each other. If we all agree no more killing for our warlord, nobody dies anymore. Maybe we go check out Proxima Centauri together?
https://brilliantmaps.com/europe-fight-war/
Results are heavily dependent on how you ask and the context of current conflicts.
I am honest enough to refuse military service if I don't have a horse in the race so to speak. That can be a constitution that grants rights, it could be land or political participation, the vastly more important reason would be if friends or family that are threatened. Without any of that there is little to be gained and I believe many soldiers are exploited and dependant on the income. But it is a bad trade in many cases.
But for active military participation few conflicts would qualify to convince me to take up arms. I am not from the US but a relatively wealthy country. Some might see that as decadence and lacking thankfulness for the opportunities the country is granting me. But in a lot of cases wars aren't fought for soldiers, just by soldiers. And if I have the impression that the leadership isn't honoring civil liberties, the countries constitution or values, I am not putting my life on the line for it. In the end it is a decision for what you would exchange your life because you have to accept the possibility of death.
Willing to? I think yes, probably quite a few are willing. (No, I have no stats to prove it...)