Depends on what the stakes are. I think the public was aware of what the stakes were of losing WWII and were willing to endure what it took to win. Remember, the United States was coming out of an isolationist period during the 20s, 30s, and 40s. We didn't get involved in WWI until late. We didn't get involved in WWII until Pearl Harbor was bombed and even then some wanted to fight Japan only. Yet we knew what the stakes were.
I think you're dead wrong that the public wouldn't want to fight Russia if they mounted an invasion of Europe, and after 10k losses would say "Who cares, let them have it all the way to Spain." But in no universe is that going to happen, so it isn't even worth debating.
They aren't willing to endure very much when the stakes aren't high or are unclear. Why should they be?