1.5K resistor would be fine at 12 v - just a bit less current and a slightly dimmer light.
1K at 12 v, minus the approx 2v LED forward voltage means 10 mA though the LED. 1.5K would give 6.7 mA
Your average small LEDS can handle 20 to 30 mA max, so .the resistance value is chosen large enough as Andrew points out to avoid exceeding that, while small enough to give usable brightness. 6-10 mA will give usable light.
You're hardly ever going to be looking at these LEDS, so a bit dimmer isn't going to hurt.