I found the What-Is-It forum Feb. 11, 2012 post which shows an object very similar to your "button."
http://www.treasurenet.com/forums/what/282503-possible-civil-war-button-pre-cwe.html#post2676026
Unfortunately, that object is missing its back, so no help there.
But the "eagle walking on bunched arrows" emblem on it seems to be identical to yours, or very nearly so. Please compare it with your "button" and let us know whether the emblem is identical or not.
As I mentioned, the back of your "button" does not have a typical button's attachment-form, such as a loop or shank. It looks more like the back of a rivet-button, with the rivet-flange broken off. What is the diameter of your "button"?