Democratic Party: "Working America" (Urbanites, Union members, ethnic and religious minorities, working class and lower middle class Americans, liberal intellectuals, social conservatives)
Republican Party: "Professional America" (Suburbanites, White collar workers, WASPs, upper and upper middle class Americans, professionals, social liberals)
American Party: "Angry America" (Rural Americans, low-wage laborers, WASPs, lower and lower middle class Americans, social conservatives, farmers)
The Civil Rights movement plays out so that both major political parties unite to oppose southern backlash, rather than the Republicans feeding on it, leading to the development of the 'American Party', a right-wing populist movement dominant in the South and in some parts of the midwest amongst working class voters.
The Democrats have largely kept their working class base and still capture most of the Catholic vote. The party is about evenly split between hawkish, social conservative Democrats and between dovish, social liberals, but both wings of the party agree more broadly on center-left economics and establishing a larger welfare state. The current President of the United States, Al Gore, is somewhere between the social conservative hawks and the social liberal doves.
The Republicans shirked away from capitalizing on racial backlash in the sixties, and as a result, preserved most of their coalition from that era. As a result, there is a significant liberal wing within the party (at least on social issues) and quite a few midwestern doves remain, as well. The last Republican President, Clint Eastwood, combined social liberalism of New England Republicans with the center-right politics of his native California.
The American Party was formed out of George Wallace's Presidential bid in 1968, and broadly defined, it is a right-wing populist party. Isolationist, protectionist, vaguely racist, and xenophobic, the American Party plays the role of kingmaker in Washington, though more often than not it does so in favor of the Republican Party, much to the chagrin of its rank-and-file. The American Party has been declining substantially in recent years, and with the die off of the baby boomers, it'll probably be gone completely. It's latest Presidential nominee was Ron Paul of Texas.