Well, back then the Democrats represented a broad middle class, with a base of factory workers, many of them unionized, and the party had to be smart, especially in the courts, to overcome the natural advantages of the owner class. In contrast, the Republicans looked like a claque of country club drunks who staggered home at night to sleep on their moneybags. Bad optics, as we say nowadays.
The Democrats also occupied the moral high ground as the champion of the little guy. If not for the Dems, factory workers would be laboring twelve hours a day and children would still be maimed in the machinery. Once the relationship between business and labor was settled in the 1950s, the party moved on to a new crusade on even loftier moral high ground: civil rights, aiming to correct arrant and long-lived injustices against downtrodden black Americans. That was a natural move, considering America's self-proclaimed post-war status as the world's Beacon of Liberty. It had to be done and a political consensus that included Republicans got it done. Consensus was still possible.
The Dems built their fortress on that high ground and fifty years later they find themselves prisoners in it. The factory jobs all vamoosed overseas. The middle class has been pounded into penury and addiction. The Democratic Party split into a four-headed monster comprised of Wall Street patrons seeking favors, war hawks and their corporate allies looking for new global rumbles, the permanent bureaucracy looking to always expand itself, and the various ethnic and sexual minorities whose needs and grievances are serviced by that bureaucracy. It's the last group that has become the party's most public face while the party's other activities – many of them sinister — remain at least partially concealed.