The government spending category that matters in the context of this article is social spending. It absolutely dwarfs military spending and has ever since the end of WWII. Moreover, if you want to look at trends, social programs have been rising for the last half century while military spending has been falling as a % of GDP.
Liberals always frame economic discussions with military spending as the "expensive" thing that is dragging us down and causing our deficits. But that's only because they remove social spending from the equation first. For liberals, social spending is the reason they exist - so it is not on the table. With social spending out of the picture, then yes, military spending becomes the biggest remaining nut.
However, if you look at government spending not from a liberal's eyes but from something more rational like, say, a spreadsheet, you will find that social programs cost 4 times more than military programs ($0.5 trillion vs. $2 trillion) each year.
This makes it very hard for me to get worried about the "military-industrial" complex. Personally, I worry about the biggest guy in the room and if you take your liberal sunglasses off, that would be the socialist-political complex, not the military-industrial complex.
Ike was concerned that the struggle with communism would require a continuing military expansion for decades to come and we had to be careful not turn into a military state. I think we've done well in that regard. The president doesn't wear a uniform and the welfare state is way, way ahead of the military state.