Thanks for getting me up right . LOL ! Eagle is interesting I hadn't looked at it that way . I think I see a stag looking to the right . This Vermont button is the closest image I can find that is similar.
DiggerDad, your guess is "close"... the emblem is indeed a stag's bust, but the "bar" is what in Heraldry is called a Torse, which is a coiled wreath viewed on edge. You've found a pewter Livery button. I didn't find a match for yours among the many stag-head/bust Livery buttons at the link below, but the photos there will show you the 6-twist Torse in better condition. https://sites.google.com/site/liverybuttonsidentified/home/stag-head
Ooops... I must confess I failed to pay enough attention to the photo showing the pewter disc next to a ruler. At 2 inches wide (or a bit less), it's more likely to be a Livery horseharness rosette than a button.