Defense will pay for itself through economic stimuli.

... and other fantastic stories

It's basic keynesianism.

That would suggest either basic Keynsianism or your understanding of it is wrong. Resources directed towards the military (with the exception of research) represent almost pure waste from an economic perspective.

You've got a bunch of poor people starving and set up a factory to produce a couple of bombs and pull some farmers off the land to have them march up and down the parade grounds. That isn't going to put more food on the table. Sure it might be a good idea regardless because being invaded sucks, but it isn't wealth creation without a very creative understanding of wealth. A society can't be better off without creating new wealth.

Said poor farmers will make better salaries, which they will spend in the economy, which drives growth for everyone.

How do you figure that? This is literally telling some of the people who would be growing the economy to stop doing that and focus on making military goods instead. That can't be done and also have a stronger economy. The resources for the army have to come from somewhere - they're resources being directed away from strengthening the economy towards strengthening the army.

I suppose there could be some sort of plowshares-to-swords program where they build tractors and bulldozers that can be repurposed into military gear on short notice. But I havn't heard of that working anywhere before and my read of modern militarys is that the gear gets pretty specialised to military use. And the soldiers need to actually focus on soldiering rather than being part timers.

At some level a country needs an army because without one they don't get to have an economy, but it is a dead weight in terms of prosperity. Military expenditure comes directly out of what people would otherwise use to improve their own lifestyles.