I remember this much of the song from when I was young:

My Daddy is President.
What does your Daddy do?
We live in a big white house
On Pennsylvania Avenue.
When we play Hide 'n Seek, it's with Secret Service men
'Cause my Daddy's the Pesident.

I remember it playing on the radio, and it seems to me that it played through twice, with an interlude between two verses, but I can't recall any of the second verse (which replaced the "Hide 'n Seek" part.) I also still remember the tune!