I still think it was a battery. I've got a toy kangaroo like that - you push the paw and it hops around, singing "Waltzing Matilda". There's a battery plack under the skin, but it causes a square bulge.

Of course I'm not suggesting Bush would do anything like that. I imagine he'd be more likely to cry out "You can run but you can't hide", at random intervals, or make comical faces.