This is a book for people with low blood pressure, because if reading it doesn't get you riled up, I don't know what...
Here's the story, in brief:
In the early 1900s, the American South was really, really poor, and the poorest people there were the blacks, to a large extent eking out an existence in poorly paid jobs as agricultural (to a large extent seasonal) workers or house servants. During the New Deal, the federal government did try to do something for the people who were suffering economic hardship, and a sort of coalition emerged where northern Democrats wanted to help working-class families and southern Democrats also wanted to help working-class families – just not black ones. Hence, the southern Democrats in Congress, who had tenure and lots of experience in political wheeling and dealing, thanks to having rather safe seats, thanks to the massive disenfranchisement of the South's black population, guided legislation through Congress that would get lots of federal money into their states, but keep federal bureaucrats – who might insist on rules being enforced fairly and equally for both blacks and whites – out of the actual administration of the aid. This was later repeated with the G.I. Bill, much to the detriment of black veterans. With administration of the bill largely decentralized to local white officials, bankers etc, they were largely screwed.
All sorts of dirty tricks were used. Unemployment benefits? Well, sure, you can get them… but you have to have had continuous employment to qualify. So you're a black agricultural laborer who only gets badly paid seasonal employment? Well, tough on you then. And besides, if they get unemployment benefits, they might not want to get back to back-breaking work for a pittance of a salary.
Social Security benefits? Well, sure, you can get them… unless, of course you're domestic help or work in agriculture, the two areas where blacks were hugely overrepresented.
Minimum wages? Well, fine… But not across racial lines down here in the South, where that would mean having to pay blacks much more than today – or, to quote Florida Rep. James Mark Wilcox:
“There has always been a difference in the wage scale of white and colored labor. So long as Florida people are permitted to handle the matter, the delicate and perplexing problem can be adjusted; but the Federal Government knows no color line and of necessity it cannot make any distinction between the races (...) You cannot put the Negro and the white man in the same basis and get away with it.”
Etc. The federal government and the northern Democrats went along to get something done, at least, and the South profited mightily from the inflow of capital – but the black population was seriously underrepresented among those who gained from this aid.
Unions were very important to non-Southern Democrats representing large industrial constituencies, and the South was willing to support their wishes for union and labor rights provided the statutes didn’t threaten Jim Crow. Southern incumbents traded their votes for the exclusion of farmworkers and maids. But as unionization threatened to fuel civil rights activism, they joined with northern Republicans to crack down on it with the Taft-Hadley Act, which helped stop unionization in the South. Instead, unions would concentrate on areas where they were already strong, and instead of fighting for a more advanced welfare state for all Americans, negotiate with employers to secure private pension and health insurance provisions for union members.
Like I said, this is a book to raise your blood pressure. But does it make the case for current affirmative action? I don't know, really. There are so many poor and generally underprivileged people in the USA today that perhaps you should just target programs according to income level or somesuch – but be prepared for the current Republican party to racialize the issue anyway, like for example Ronald Reagan did in his campaigning, talking about "welfare queens" and "young buck". As can be seen from some of the responses to Barack Obama being elected president, racism and race-baiting is still a powerful force that can be used for populist purposes if you don't have any policies to offer that actually make sense.
(Here's a review by somebody far more knowledgeable than I on these issues. And here is another one.)