Great job gentlemen!
I combined mantoui's updated OneWire::write_bit function along with the changes made by alvesjc and I'm now able to run the DS18x20_Temperature right out of the box.
This effort should go a long way in getting other people moved over to the Due because so many projects have requirements to read temperatures and interact with other one wire devices.
Thanks for all your help in getting this working.
I've put all the stuff in a zip file for others to test without having to edit the files.
OneWire.zip (14.9 KB)