Economical liberalism calls for the cutback of the state, social democracy calls for the growth of the state in order to improve people's lives.
There were no crisis in the Left until the 1980s that would make them embrace the Third Way, neoliberalism with a human face.
So, to conclude, economic liberalism and social democracy in the same party is clearly contradictory in a mid-20th Century context.
That was OTL, you can't apply OTL here, Erhard was never meant to get to the Chancellorship, but Schumacher was assassinated and he assumed leadership, it caused a crisis in the SPD due to his more liberal stances.