Sugar Babe (if it is the same song you're looking for) was in the New Lost City Rambler's songbook from (the 70's?). Here's what I recall:

I'm going back to Mexico, sugar babe (x2)
I'm goin back to Mexico,
And I'm gettin married fore I go, sugar babe

Whatcha gonna gonna do when the well runs dry, sugar babe (x2)
Whatcha gonna do when the well runs dry
Sit and watch those crawdads die, sugar babe

Whatcha gonna do when the meat runs out, sugar babe (x2)
Whatcha gonna do when the meat runs out,
Sit in the corner with my mouth poked out, sugar babe

Whatcha gonna do when the meat comes in, sugar babe (x2)
Whatcha gonna do when the meat comes in
Sit in the corner with a greasy chin, sugar babe