What is the origin of the phrase "A Mountain I'm Willing to Die On"?

I hear the phrase "A Mountain I'm Willing to Die On" too many times at work and figured it meant "is this the battle I choose to fight today"? But this is used too many times on the interwebs to google down to the origins of it. Can someone point me to it?

The phrase is a slight variant of "Is this the hill you want to die on?" which is often used in the military when discussing holding a position at all hazards. In this case, the answer is assumed to be "no".

When you decide to defend the spot to the limit, then "No better place to die" is often used. I have heard this used for many actions, back to the US Civil War and it probably was old during Ancient times.

As Oldcat's answer points out, the original wording of the phrase seems to have involved a hill rather than a mountain.

Both the Korean War and the War in Vietnam involved significant battles over hills that in some instances were taken at great cost only to be abandoned shortly thereafter because their only military significance had been the presence of enemy soldiers on them.

Tim Carew, Korea: The Commonwealth at War (1967), for example includes this comment on hill fighting [combined snippets]:

Like thousands of other hills in two world wars—in Africa, Italy, North-West Europe and Burma: hills to be clawed up by painful inches in the face of lashing fire and hails of hand grenades; to be captured and held; to be endlessly and backbreakingly dug and wired, for work on defensive positions was never finished; to be shelled off, overrun and re-taken; to be buried alive on or to die on—hills with names like Pork Chop Hill, the Punch Bowl, Frostbite Ridge, Old Baldy, Bloody Ridge and The Brown Bastard; hills which became ...

One early instance of the full expression appears in Carolyn Denham, "Can Politicians Trust Evaluators? A Case Study of ECE Evaluation in California," in The Phi Delta Kappan (April 1976) [snippet]:

...an emotional defense of the [Early Childhood Education] program by [Wilson] Riles in testimony before the subcommittee, According to Riles, "You can't choose to die on every hill, but this is one hill I'm willing to die on."

The quotation from Riles seems to have come from an article that Riles wrote, "ECE in California Passes Its First Tests," also in The Phi Delta Kappan (September 1975). At greater length, he said this in the article:

ECE has made a profound mark on the educational landscape. In less than two years, it has generated tremendous momentum for change. Many of its concepts are being adapted for use in the upper elementary grades and in nonparticipating schools. The impact of this sweeping attempt to revitalize public education in California is being watched across the nation.

As a result of this success, I'm willing to fight for ECE. I've been in education and politics long enough to know that you can't choose to die on every hill—but this is one hill I'm willing to die on.

But the underpinnings of the expression are evident in this excerpt from "Do it" (1972) which is either the name of the original article or the name of the publication in which it appeared, reprinted in the [Canberra, ACT] Woroni (March 11, 1985):

Why does grass inspire the Viet Kong and kill the fighting spirit of the American GI? Any pot-smoker can understand it; Marijuana is a truth serum. The Viet Kong are defending their parents, children and homes — their deaths are noble and heroic. The Americans are fighting for nothing you can see, feel, touch or believe in. Their deaths are futile and wasted. 'Why die on Hamburger Hill?' asks the pot-smoker American soldier, as he points his gun at the head of the captain who ordered him to take a hill that only the Viet Kong want.

By 1984, the expression had been appropriated by people writing about corporate career success. From Michael Cohen, Employee Handbook for On-the-Job Survival (1984):

What is my chance of winning if I engage in a "toe-to-toe" battle with my co-workers or boss on this issue? Is this the "hill I am willing to die on"—the one I am willing to go down fighting for? In the normal course of the day, when confronted with a problem, it is not realistic to expect someone to run down this entire list of questions. But it is always helpful and productive to review these issues before deciding on a course of action.

The only explicit connection I've seen made between the expression and a particular military engagement occurs in a sermon by Anton Bosch, "From Hamburger Hill to Calvary," published in July 5, 2016 on SermonIndex.net:

The Battle of Hamburger Hill was a battle of the Vietnam War that was fought by the United States and South Vietnam against North Vietnamese forces from May 10–20, 1969. Although the heavily fortified Hill 937 was of little strategic value, U.S. command ordered its capture by a frontal assault. The hill was finally taken at the cost of 72 Americans killed and 372 wounded. Losses on the North Vietnamese side are estimated at more than 630 dead.

What makes this battle so significant is that the hill was of little strategic value, which was proven by the fact that it was abandoned by the US forces two weeks later. But more significant is the fact that the fall-out from this battle back home forced the Nixon administration to order the end of major tactical ground operations in Vietnam. So in a sense the hill and the battle were won while at the same time losing the war!

...

It is vital that we choose our battles, or put in another way, choose which hill we are willing to die on. Dying for something that in the end is not important is a waste of a life. If one is going to give one’s life for something, surely one needs to make sure that it is for the right reasons and the right cause. And if you are going to expend resources, surely you should make sure that they are being spent in the best way possible. Jesus said: “do not… cast your pearls before swine…” (Matthew 7:6).

The earliest instance I've been able to find in which the hill becomes a mountain is from Bill Alexander, A Father's Book of the Spirit: Daily Meditations (1997) [snippet]:

What is the mountain you are willing to die on? The senseless preservation of self does great harm to the father and to the children.

In every case, the implication of "a hill [or mountain] that one is willing to die on" is a goal, principle, or cause that one believes so deeply in that one is willing to make a great sacrifice (figuratively, one's own life) on its behalf.