In Heinlein's book TEFL is the Pawn Shop song and actual song and if so what is the title or tune?

"The Pawn Shop Song" may have more than one source.

The lyrics are reminiscent of "Pittsburgh, Pennsylvania," written by Bob Merrill in 1952. The scansion is slightly out and the coda in "Pittsburgh, Pennsylvania" has no correspondent in "The Pawn Shop song" but there are significant similarities.

A closer fit for the tune is Malvina Reynolds' "Little Boxes" published in 1962, which meshes nicely with nearly all the verses of "The Pawnshop Song" but shares no correspondence of lyric.

As the tunes of both songs closely resemble each other and predate TEFL by at least 11 years, RAH could have used both as his model for "The Pawnshop Song," taking what he liked from each. He was good at that.