One of a couple of things:
try wiggling the switch stalk, if it starts working, possibly a faulty switch.
if no workee, try tapping on the hazard switch, that's also the flasher relay on the new beetle, if that works, you may need a flasher switch, which I would highly reccomend NOT trying to do yourself as it is almost guaranteed that you WILL break something as the center dash sections are kinda tricky to remove.
Last, if they blink a couple of times and then stay on, not flashing, try smacking each turnsignal housing on the lense one at a time.  sometimes the sockets that hold the bulbs go bad.