From the star charts I've seen, the Federation doesn't exactly dwarf the Romulan Empire, but is just a bit larger. (I don't know if these charts can be considered canon, though.
I get a sense that by the time of TNG, most Federation member planets are a bunch of freeloaders. It's the humans that do most of the work.
They don't really start building warships until they realize how dangerous the Borg and Dominion are.