At first glance, the spread-winged eagle makes your button resemble an American military button... or a US Government Official & Diplomatic Service button. (See the Albert book's "OD" section.) But in actuality, it is a Livery button. Note that the eagle is NOT holding an olive branch or arrows in its talons, doesn't have a Federal Shield, nor stars around it. It is "just" an eagle (or similar bird)... and it is displayed above a Torse, which is a symbol frequently seen on Livery buttons. A Torse is a spiral-bodied wreath seen laying HORIZONTALLY below the main emblem. (In other words, it is a "side-view" of a wreath.) A Torse is not "the ground" under the main emblem, or in this case, the eagle. The photos below show Livery buttons which have a Torse under the main emblem.
For anybody here who doesn't already know:
Livery buttons were primarily European, and they showed the Family Crest of a Nobility (or merely wealthy) family. They were made for use on the uniforms of the family's household servants, such as butlers and coachmen. Livery buttons date from at least the 1700s and are still in use today.