I found this in Hard-Hitting Songs for Hard-Hit People. It's just a little two-line tag that leads into the chorus again:

'Cause the governor on the radio today
Jumped up to the microphone and he did say:
CHORUS

The song was copyrighted in 1961 and 1963 by Ludlow Music. It was written a lot earlier than that, but I don't know when. Alan Lomax makde Woody's Library of Congress recording of the song was in 1940.
I couldn't find any background information on this song. One book said it "was one of Woody's finest Dust Bowl ballads." That's all they said.

The Library of Congress recording has this alternative second verse:

You want to buy a house or a farm, that can't do nobody harm
Or take your vacation by the mountains or sea
Don't swap your old cow for a car, you'd better stay right where you are
Better take this little tip from me:
'Cause Governor Merriam on the radio one day,
He jumped up to the microphone and he did say:
[chorus]

I found an interesting piece of information at a site that gives the history of the Governors of California (click). Frank Merriam was Governor of California 1934-1939, While in office, he "'resembled [Californian] President Herbert Hoover in his conservatism over what must be done to fight the Depression.' As acting governor in 1934, he sent the National Guard to San Francisco during the July waterfront crisis even though Mayor Rossi did not request them."

-Joe Offer-