"A liberal has core beliefs. How in the world can we change a liberal to a more moderate or even conservative position if they only stick to their core beliefs?"
We can change their core beliefs by repeatedly showing them the errors in their logic. When they make decisions based on feelings point out to them how logic would require them to rethink their positions. You have to be patient with them, because liberals are used to deciding things based on feelings, not logic.
Another is if you run a clearly conservative candidate they will always win. I see we have the distinguished gentleman from Illinois Senator Alan Keyes.