The core belief would be not to turn and run once you're in a war. Fair enough. But if people expect you to get us into situations like this when we don't have to -- if prudence in foreign affairs isn't a core principle -- they may vote for the other side.
Here's what I think is the difference on war. Conservatives think that America and American values are valuable and worth fighting for when America's vital interests are threatened, while too many progressives do not think our nation are heritage are worth fighting for. But that doesn't mean that there's some conservatives who feel that America does not need as many vital interests as others do.
Another way I think of the divide is that there's some conservatives who are wary of war because they are afraid we might lose, while too many progressives would avoid war because they are afraid we'll win.