Ideally attract the core voters but to win an election the party that attracts the centre / floating voter wins. I think it's a mistake to chase the liberal voters but the message from the doorsteps before the last general election from people who said they were voting LibDem (certainly in the less affluent parts of town) was that the believed LibDems were further left than Labour.
Labour members left the party (or at least became less active) during the Blair years because of a move to the right and LibDem members are now doing similar.