If the processor is a PIC type, the max output (source or sink) is 25mA. At least it is for the 16F690, which I just looked up.
If the LED is the bipolar type (2 LEDs in parallel, oriented oppositely, with just 2 leads) then you can easily drive them off a single pin if you use a circuit similar to Bill_Marsden's middle diagram, but with lower resistance values, say 100ohm. That gives you the Thevenin equivalent of a connection to half the voltage via half the resistance, and your LED should work on that if the power supply is 5V. But it's inefficient in power use, as the resistors conduct all the time.
If you have the 3-lead kind of dual LED, I think you're stuck. You need 2 processor pins to drive it.