The book deals with that subject as well.
The author discusses how WPA and other monies were dispersed in critical swing states, how various departments used those funds to promote their chosen candidates and how those who were assigned jobs were expected to make contributions to the Democrats. They also tell of large amounts of cash dispersed or jobs offered in late September to October time frame, only to have those jobs go away in December.
I also suggest a reading of the book.
When you win the way FDR did, there were no critical swing states. He absolutely obliterated the GOP.
My great aunts and uncles and other extended family on my Father's side were beneficiaries of this system. As Southerners, they were by definition Democrats, but they came from a politically active and connected family, so got more than their share. In return for their loyalty and contributions, jobs were showered on them: music, art, and journalism grants via the WPA, patronage jobs in D.C. Those few still living revere Roosevelt and the others praised him until their dying day. My mother's family were just poor dirt farmers with no connections. They got nothing.