As a small farmer, Mr. Cunningham would have found himself in an extremely difficult financial situation, especially during the era of the Great Depression. What little crop his land produced would not have been barely enough (if that) to generate the revenue necessary to feed and clothe his family. In fact, Cunningham was unable to pay a legal fee to Atticus Finch in cash; Atticus accepted alternative payment from Cunningham and never doubted that he would be reimbursed for his time and effort.
"Not in money," Atticus said," but before the year's out I'll have been paid. You watch."
We watched. One morning Jem and I found a load of stove wood in the back yard. Later, a sack of hickory nuts appeared on the back steps. With Christmas came a crate of smilax and holly. That spring when we found a crokersack of turnip greens, Atticus said Mr. Cunningham had more than paid him.
Clearly, Mr. Cunningham was an honest man who did his best to provide for his family. However, his financial concerns would have lessened had he chosen to conform to society and do as he was told in order to obtain a job with the WPA. However, accepting a job provided by the government would have meant that Cunningham would have been expected to vote for politicians responsible for the program, as well as be supportive of other steps taken to aid the economy, whether he truly approved of them or not. Cunningham was not willing to sell himself for the promise of financial rewards; he remained true to himself.
To Kill a Mockingbird is set during the Depression. The WPA (Works Progress Administration) was created in 1935 in order to provide assistance to those suffering because of the economic disaster at the end of the 1920s.
If the Stock Market Crash of 1929 was not enough to hurt the people in the imaginary town of "Maycomb," devastation from the Civil War is also still felt here, as the "War Between the States" has not yet been over for a hundred years, and there are still those alive in Maycomb that have not forgotten—or been able to ignore—the scars of the war; in the novel, the communities of the South are in some ways still reeling from the destruction of a society that was agrarian in nature, and dependent upon slave labor for its success. This mentality is still evident in the terrible way a good part of the white community of Maycomb treats the members of the blacks in the town.
The quote means that if Mr. Cunningham was able to keep his mouth shut and his opinions to himself, he could probably get a job with the WPA. This would be helpful since the Cunninghams are so poor. However, as noted in Chapter Two, working for the WPA meant leaving his farm. Atticus tells the children that the farmers were hit harder by the Crash than anyone in Maycomb, and Cunningham's farm is mortgaged to the hilt: he barely holds onto it by keeping up with tax payments. However, Cunningham would do anything to keep his farm, and in doing so vote as he chooses (which is a way he can let his feelings be known).