The version I heard in the '40s was:

I don't care if it rains or freezes
I am safe in the arms of Jesus
I am Jesus' little lamb
Yes, by Jesus Christ I am


which sort of goes with:

Jesus hates me, this I know
'Cause my rabbi told me so.

or

I am Jesus'little sunbeam
And a fine fucking sunbeam am I

or

Stay with God! Stay with God!
Jesus on the 5-yard line,
Moses doin' Goddam fine
Stay with God! Stay with God!
Highty-tighty God Almighty
Stay with God!
(to the tune of Tammany)