Don't know why the stop in Waco...but hey.
Leaving Illinois the end of December I'd recommend you head straight to Quartzsite because the major festivities happen during January and the RV Show is mid-January. It's a fun time to be there to check out all the RVers. January in Quartzsite can be 70 deg during the day and around 40-50 deg at night. As you know, weather is not predictable and colder temps are possible in the desert. Regardless, at least you'll have SUN, which helps a lot.
Stay in Quartzsite until you tire but come March it starts getting very hot and folks start leaving (even during Feb). Then work your way back into other areas of Arizona that you want to explore. Spring flowers begin any time from mid-February on and sometimes in January. New Mexico is a lot colder in winter than Arizona - even the southern half so catching it on your return in April or May would be a lot more pleasant and you'd be able to get further north in NM.
Have a good trip!