It's very hard to say, it partly depends on the player. There's, what, 35 merchants plus the scavengers who hold between under a hundred to several hundred caps, then there's the caps to be looted. The merchants restock every day and get more caps, so the more you trade with them the more caps there are.
At any given moment, not including what the player holds, I'd be surprised if there was more than 50k caps floating about.