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Looks like you found an "unlisted" (not shown in any button-book) variation of the Albert button-book's US Navy NA-38, which shows an eagle with a spade shield on its chest and an oval shield on its left wing, surrounded by 16 stars. NA-38 dates from sometime between 1802 and the late-1810s. Your button's emblem has both the spade shield and oval shield, so it is probably from the same time-period as NA-38.
More photos might settle the question of whether that's a stretched-out button loop on the back, or a bent & partly broken-off "pin." At this point, I'm guessing button-loop.