I would have used the LM1117 instead. See my design here:
http://faq.auto.light.tripod.com/signal-leds.htm (There is also an LM317 design on that page.)
But more importantly, remember that it's current that matters when driving LEDs, not voltage. Just having a constant 12V source isn't going to protect you from overdriving your LEDs, you need constant current. You can find my constant-current design by following the above links as well, and it's also discussed in this forum.