It does seem like the entire budget is more broad than simply number of troops, perhaps it includes all of supplies and or fort/garrison matinaince, and of course the naval forces.
That being said, i did notice a couple ovbious things hat i guess simply passed me by the first time. Great britain ovbiously has a huge navy, and this accounts for alot of the military expenditure. Also, i noticed that she starts out with a military budget of $299. But after disbanning most of my large armies, and one small navy (north america station) i was able to get the budget down to $147.
So it does seem to be working properly, im anxious to run myself into debt now and see what you mean by "no real drawbacks to being in deficit" as this seems to be the case in real life, especially in the united states. Ovbiously you cant recruit new units, but if your standing army is say 300,000 anyways, there would be no real need for new brigades. Except for latter on in the game losing the ability to build new ships, forts, or more modern army?