I’d argue that right up until the three way brawl that was Taft V Roosevelt V Wilson, the Republicans were very much the party of the people. Roosevelt split the party, and all the lefties left the party, mostly to become Communists. Then the 1950s and 1960s happened and the Republicans leap frogged over the moderate right wing Democrats to leap head long into right wing extremism.

Admittedly that was only the first 50 or so years that the party existed.