This song first gained wide popularity in the late 1940's or early 1950's courtesy of The Weavers. I remember hearing it on radio then.

And, of course, there is also the Allan Sherman "version:"

Harvey And Sheila Lyrics by: Allan Sherman Music by: Lou Busch
Recorded live at Allan Sherman's Birthday Party (Nov 30, 1962)
from "This time, Allan Sherman's Mother Proudly Presents:
Allan Sherman: My Son, The Celebrity" ©1963 Warner Bros. Records, Inc.

Harvey and Sheila, Harvey and Sheila, Harvey and Sheila,
Oh, the day they met.
Harvey and Sheila, Harvey and Sheila, Harvey and Sheila,
No one will forget.
Harvey's a CPA.
He works for IBM.
He went to MIT and got his PhD.
Sheila's a girl I know,
At B.B.D.& O.
She works the PBX,
And makes out the checks.
Then came one great day when
Harvey took the elevator,
Sheila got in two floors later,
Soon they both felt they were falling,
Everyone heard Sheila calling,
"Ring the bell,"
But they fell.
Harv and Sheila fell in love.

Harvey and Sheila, Harvey and Sheila, Harvey and Sheila,
Chose a wedding ring.
Harvey and Sheila, Harvey and Sheila, Harvey and Sheila,
Married in the spring.
She shopped at A & P.
He bought a used MG.
They sat and watched TV
On their RCA.
Borrowed from HFC,
Bought some AT&T,
And on election day, worked for JFK.
Then they went and got a
Charge-A-Plate from R.H. Macy,
Bought a layette, pink and lacy,
Then they had twin baby girls,
Both with dimples, both with curls,
One named Bea,
One named Kay,
Soon they joined the PTA.

Harvey and Sheila, Harvey and Sheila, Harvey and Sheila,
Moved to West LA.
Harvey and Sheila, Harvey and Sheila, Harvey and Sheila,
Flew TWA.
They bought a house one day,
Financed by FHA.
It had a swimming pool, full of H2O.
Traded their used MG
For a new XKE.
Switched to the GOP,
That's the way things go.
Oh that Harvey he was
Really smart, he used his noodle.
Sheila bought a white French poodle,
Went to Europe with a visa,
Harvey's rich, they say that he's a VIP!
This could be,
Only in the USA!