First, wars are not fought that way anymore. No need for lots of tanks and ships and uniforms and the list goes on. Second, infrastructure is an admirable undertaking... just ask the Romans. Third, it is my humble opinion that what lifted us out of the Depression was a combination of a few things.
One... millions of able-bodied people were removed from the labor pool and sent to wage war. Two... these people were replaced in the labor pool by what was left. Three... waging war and supplying our allies created huge demand for goods that... because of the location of the war... pretty much could only be made here. Four... patriotic Americans dug as deep as they could to buy war bonds and fund our government.
Now, I have presented all of that to say this... realizing that I am on the edge of advocating communism with this thought... perhaps what we need is government conscription of millions of people to wage peace and prosperity... Right... Let's try this on for size...
These millions of people (and by the way, I mean everyone, not just males, not just females, not just mentally sound, not just black, white, green or orange -- if you don't have a means of employment, tag, you're it) are conscripted and categorized by the skill set for which they show promise. Some folks are good at building things, some are good at designing things and some are good for the most basic and menial tasks. They are then trained, clothed, housed and sent out into the world (or across the US) to build a road, dig a well, discover useful plant life... etc. Kind of like a military version of civilian life. And, the conscription would be a three year mandatory at the end of which you could choose to re-up or move back into the civilian (read not government) sector.
Just another random thought.