The sad thing is that wars can popular at the time, when it looks like your side are big enough and the other side is small enough, and your side is going to win without too much impact on civilian life, including young men coming home in bodybags. Wars like that win elections, and that's largelyn what they are for.
The war against Argentina was like that, so was the Gulf War (which I suppose should be referred to as the Second Gult War - the first one being the war by Iraq against Iran, and the third being the little unpleasantness a few months back which temporarily took the heat of the Lewinsky headlines). So was Vietnam, to start with. So was Afghanistan, to start with.
So were most Colonial Wars, to start with, and often to end with, because most times the big guns and the big guns win in the short run.
Chechnya probably won't be Russia's Afghanistan, there's no big friendly superpower supplying arms, and no safe haven. It probably will be Russia's Ireland, which means it'll be a long long time before it's over, and it'll flare up again and again. And in the end Russia will pull out.
That's unless the Russians follow the American example with defeated nations within their territory, and I can't see that them getting away with that.