We are going pretty far down a rabbit hole with this ... but to think out the hypothetical:
Before Russia could invade Turkey with a large force, Russia would need to mass a large force on/near the Turkish border. The U.S. has satellites that monitor Russian troop movement; the U.S. and its NATO allies also have spies who would hopefully tip us off to plans. We would most likely have some time (days at least) to prepare.
As you say, we could not move a force sufficient to defeat a 1,000,000-man Russian invasion force in days; however, we could, and would, move thousands of troops into Turkish border regions (I personally know of two brigades that could be there within 18 hours, and there are more). We could, and would, move carrier groups to the region. We could, and would, warn Russia of a severe military response through diplomatic channels and/or publicly. We could, and would, start the process of moving a force sufficient to defeat the Russian invasion force toward Turkey - it could not arrive in time, but it would arrive eventually, sure as death, and Russia would know that.
If Russia invaded Turkey, most likely, it would win the battle, lose the war. Since Russia is not very dumb, they would most likely not go through with an invasion of Turkey once U.S. forces were inserted into Turkish border regions.
I'll note again that Britain is a reliable ally, and in this hypothetical situation, I am sure that Britain would also insert troops and otherwise make it clear that the invasion would ultimately fail. I am also sure that Germany would dither, trying to be a go-between rather than acting as a NATO ally ... and I am sure that France would bloviate and do little or nothing.