I think that's the exact opposite of what's written.
"Within every district to which a federal collector would be allotted, there would not be less than thirty or forty...whose influence would lie on the side of the State."
I guess you're right -- the "districts" in question are subsets of States, so he's saying something like "for every one federal official in Phoenix, there would be at least 30-40 Arizona officials".
"Within every district to which a federal collector would be allotted, there would not be less than thirty or forty...whose influence would lie on the side of the State."