In the version of “Talking Union” that's on Pete Seeger's Greatest Hits, Seeger explains the origin of the song. I can't find a transcription of this anywhere on the web, so here goes:
This song was written by Mill Lampell, Lee Hays, and yours truly, Peter Seeger, in the spring of 1941. That was the year that Henry Ford was being organized into the CIO.
And Woody Guthrie had taught the three of us the old “Talking Blues,” you know: “If you want to get to heaven, let me tell you what to do: got to grease your feet in a little mutton stew.” And I think Mill, it was, thought of paraphrasing that, and Lee added a verse and I added a verse and suddenly we had the song almost completed, except that we hadn't found any solution; all we'd done is add up the problems, but we hadn't found how to solve any of them.
About a month went by; one day I was sitting up on the roof and realized that there's only one solution to it: the old one of stick together. So I made two verses to end it off, none of them rhymed, and that's how the song “Talking Union” was born.
Here are those concluding verses:
Well, out in Detroit here’s what they found;
Down in Pittsburgh here’s what they found;
Down in Bethlehem here’s what they found;
Out in Frisco here’s what they found:
That if you don’t let Red-baiting break you up,
If you don’t let stool pigeons break you up,
If you don’t let race hatred break you up,
If you don’t let vigilantes break you up—
What I mean, take it easy—but take it!
(Lyrics as transcribed from abovelinked recording; the version on the Pete Seeger appreciation website has some lines in a slightly different order.)
(Heh—I like this quote from the front page of that site: “Some may find them merely diverting melodies. Others may find them incitements to Red revolution. And who will say if either or both is wrong? Not I.” —Pete Seeger in Rolling Stone, April 13, 1972.)