The reason many 'working' people vote Republican is simply because they identify more with the Republican party than they do the Democratic.
CPT. Apathy, your analogy and your father's statement was probably based upon the Democratic Party of the 1940's and 1950's. The party under FDR, Truman and JFK was a whole lot different than the one today. Looking at their policies you would think they were more Republican than Democrat but that is how much the Democratic Party has changed.
My father was a devoted Democrat for a good part of his life, at least until Jimmy Carter was elected. A very blue collar man, he looked at the Democratic party as the protector of the working man. As the party evolved and his views were marginalized more and more he became disillusioned with the party and left. He isn't really anything anymore but I guess if you had to call him something he would be a little right of center, using today's definitition.
What is driving the 'working class' to the Republican Party is simply the fringe of the Democratic party marginalizing the core's beliefs. Union members get pretty ticked off when their dues are used to support candidates that they disagree with on many issues. It's not just one thing. Many of the working class have strong opinions on abortion, gun control, government interference, taxes, homosexual marriage, etc.
The problem is that the Democratic Party has changed so much over the last 40 years. It isn't the same party your father talks about. I have the honest opinion that the Dem. Elite doesn't dive a hoot about the average American. I am sure the Republican Party doesn't either but I never had any illusions about them.