Utilizing pull-down/pull-up resistors like this can be very tricky. You might be better off using a TTL or CMOS inverter. The circuit would be pretty simple:
Click for big version
The basic idea is that when the switch is in position 1 (and presumably closed), the inverter gets a high signal, so it outputs "0", and the red light goes off. At the same time, the green light is getting a signal, so it turns on.
When the switch is in position 2 (and presumably open), the inverter is getting a low signal, so it outputs "1", and the red light turns on. At the same time, the green light is getting no signal, so it turns off.
3.3V TTL inverters are pretty cheap (you can get them on
www.digikey.com for under a dollar, and probably from Radio Shack for under 5.) Power the circuit with two AA batteries and use some 240 ohm resistors to prevent the LEDs from burning out. If you can only find CMOS (5V) inverters, then power the circuit with three AA batteries (4.5V) and use 470 ohm resistors.
The resistor values are approximations based on what I've acutally built before...I could be way off so be careful.