https://en.wikipedia.org/wiki/War_of_1812#Unpreparedness
Apparently having a very small army didn't help when Jefferson's party wanted a war. I guess they over-rated state militias?
A lot of the founders' ideas didn't work out they way they hoped. (For example, they tried to prevent political parties and failed utterly.)
When people quote American founders out of context, it's as if it settles things, but they were just making it up at the time, often based just on what sounds good. Jefferson in particular was often a rather impractical man, but a popular politician who promoted a lot of bad ideas (and a few good ones) that made for good politics at the time. He's hardly the only one.
That was the general approach of the United States until ~ the early 20th century. Before that, the 'standing' military was generally tiny, the employer of last resort (criminals, drunks, etc.), and was greatly expanded by volunteers in times of warfare.
In fairness, if Jefferson had his way, there wouldn't be much of a military around to plot a coup in the first place.
He'd also be considered a staunch non-interventionist were he alive today - "peace, commerce, and honest friendship with all nations and entangling alliances with none." Not much use for a standing army when that’s how you see your role in global affairs.