Wiktionary confirms your first definition (2nd definition at https://en.wiktionary.org/wiki/short_of https://en.wiktionary.org/wiki/short_of - wiki's 1st and 3r

Wiktionary confirms your first definition (2nd definition at https://en.wiktionary.org/wiki/short_of https://en.wiktionary.org/wiki/short_of - wiki's 1st and 3rd definitions seem like the same thing in my mind) but other dictionaries don't seem to support this (OED only has wiki's 3rd listed) and I've certainly never encountered it before now. Odd. I would say I'm short on money this month. Etymologically my thinking was that it comes from "to fall short of" - e.g. to be too short to reach a point. Fitting your 2nd definition.