Just had a couple of brain cells kick in. The line "Jesus came to me" should be "Jesus speak (or speaks) to me." It's what could be called a "call and response" song.

The lines of the verses go:
Deedle-dum-dum deedle-dum-dum deeeee-dle) - out on the rollin' sea
Deedle-dum-dum deedle-dum-dum - let it roll...