The tire pressure on the door jam is intended to enable the prescribed tires to support the weight of the vehicle. If you use a lower pressure you will probably not have the ideal tire contact patch and you will have more sidewall flex.
Sidewall flex can lead to overheating and blowouts under certain conditions and the energy used in the tire flex decreases your fuel economy. It's a little like driving in sand if the tires are too low.
If you experiment with different sized tires you might need to adjust the pressure to have enough air to support the weight you are carrying.
Some people apparently like to use the maximum rated pressure noted on the tire (which can support the maximum weight) but this could lead to a rough ride.
Here's a web site with lot's of information on tires, etc...
Barry talks about tires and related topics.
barrystiretech.com