Pretty sure Bret Stiles was whistling the end part of the verse from "Oh My Darling, Clementine"

The song is about a bereaved lover singing about his darling, the daughter of a "49er" (a miner in the 1849 California Gold Rush) -- but also another interesting FOOTBALL theme

The singer loses Clementine in a drowning accident [I have thought there's a WATER theme going on and/or I've wondered about RJ and a FEAR of water]  -- and the singer himself tells that he could not save her because he could not swim  

THE LYRICS ARE:

In a cavern, in a canyon/Excavating for a mine/Dwelt a miner forty niner/And his darling Clementine.

Oh my darling, oh my darling/Oh my darling, Clementine!/Thou art lost and gone forever/Dreadful sorry, Clementine

Drove she ducklings to the water/Ev'ry morning just at nine/Hit her foot against a splinter/Fell into the foaming brine.

Ruby lips above the water/Blowing bubbles, soft and fine/But, alas, I was no swimmer/So I lost my Clementine.

Oh my darling, oh my darling,
Oh my darling, Clementine!
Thou art lost and gone forever
Dreadful sorry, Clementine

How I missed her! How I missed her,
How I missed my Clementine,
But I kissed her little sister,
I forgot my Clementine.

Oh my darling, oh my darling,
Oh my darling, Clementine!
Thou art lost and gone forever
Dreadful sorry, Clementine