First of all not everything on the due runs at 3.3 V. The USB chips require 5V
You can power the due directly off the USB port. But don't expect it to run a display or a lot of other gear.
You can run the due office 6v battery pack, But it requires for batteries minimal.
The regulators will accept that voltage, But it is a little close to the regulated output for me.
It is best to use a 7.5V battery pack or 9V Regulated power supply that can handle at least 1 amp.
The problem with battery packs is they rundown. And you have to replace the batteries.. This is fine
for a project that does not have access to any other power source. But if you have access to a power source,
you're better off using a 9V Regulated power supply.
Hope this helps.
Joe.