I currently have the stock size tires 265/60R18 and my 2006 Limited is AWD. I'm considering upping to 265/65R18. I've cranked up my torsion bars 1" and have air bags in the rear that even with no air have raised the rear 1".

My question is if I get a flat can I run the smaller spare without issue or will I burn up a diff or transfer case?

 

If you have a limited slip differential, both tires on that axle need to be the same size. Otherwise, it's an inch difference in diameter, you can use it, but, do not go far. Use the spare to get you to where you can replace/repair the bad tire. If you have LSD, and blow a back tire, put the spare on the front, and move the correct size tire to the rear.