In GF, when Michael returns to the Mall after McCluskey broke his jaw, Sonny says "...a hundred button men on the street..." looking for Solozzo. That had to have been only part of the Corleones' total strength.
In II, Michael supposedly is "legitimate." But, at the Senate hearing, you see an FBI chart showing a substantial number of men, called "Buttons - Soldiers," under the Caporegimes. (See p. 218 of Harlan Lebo's "The Godfather Legacy" for details.)