If that happened, the Democrats would have died and a new third party would have split from the Republicans.
Probably there would be retained a consensus on financial issues but there would be growing disagrement on civil rights...and how to do deal with the Soviet Union which becomes America's #1 foreign policy concern in the 30s and 40s without the conditions that lead to Nazi Germany.
Somehow I severely doubt there would be an end to history with the absense of the Great Depression and with that, I'll go with the above explanation.