cough Iraq War cough
Also, Western style democracies are very much "vote every X years and then do fuck all about the reps all the other times." So the actual entity in control the vast majority of the time is still a small council same as a dictatorship. If enough of them want war, it will happen and it will be pushed through legislature extremely quickly (which, I can't imagine the critical mass needed to declare war right the frick now being over 100 politicians in any Western style democracy).
Also, you're putting a lot of stock in troops moving out before a vote happens. I doubt this happens ever, except in the case of a rogue military. But if the military is rogue, then the democratic government has already fallen.