If you do that, you're just giving Russia the justification they needed to turn that kinda-sorta-cold-but-lukewarm war into a full out one.
The problem when calling bluff is that the other one can do it too. Do you thing you will get the necessary popular support for a war against Russia over some country most people never heard of? You still need some kind of Pearl Harbor to convince the people that this war needs to be fought. And after the 9/11 ruse, I think being convincing could be a tad bit difficult.