Pretty sure it's a resonator guitar, commonly called a Dobro.
The difference between an actual played flat on one's lap, or standing with a shoulder strap but still parallel to the ground, country music style 'Dobro', and a blues/folk/whatever resonator guitar, which is played like a regular guitar, is that the Dobro has a rectangular shaped neck (in cross section), whereas the resonator guitar has a regular semi-circular shaped neck (in cross section), just like any old six string.

"Dobro" is actually a trademarked brand name, but even when made by other companies (Gibson {who may have actually bought out Dobro, and hence the trademark??}, etc.) these are referred to as Dobros, much like any tissue is called a "Kleenex".
These, pedal steels, lap steels, and Weissenborns are my favorite instruments, and one day I'd love to learn how to play them.
I LOVE 'SLIDING'!!!
BTW; this fall I get to see Arlo Guthrie sing this song LIVE when he appears at our concert series.

My only regret concerning this song is that I never got to hear it's author (the phenomenal Steve Goodman) sing it live and in person.
