If it's a plastic, wooden or shell button, it may not be a problem. It also depends on the size of the button. If it went all the way down the throat (were you able to see it go down?), it may just be able to go on through. My runners sometimes eat hickory nuts and acorns. Talk about scary the first time I saw it! One huge lump sliding down that slender neck, like a snake eating a bit rat! Yow!
So how's the patient acting? Shaking the head, opening his or her bill wide, like yawning? Eating okay? Be sure there's plenty of water.
I'd be more concerned with a metal button - that might call for a vet visit.