Republicans rarely criticize Obama for lack of empathy - in part because liberals have traditionally been seen as standing up for the weak and the vulnerable. Conservatives can be just as empathetic. But they believe that in most cases it's not government's role to be the primary dispenser of empathy.
A tree is known by its fruit a man by his deeds. A good deed is never lost he who sows courtesy reaps friendship and he who plants kindness gathers love.