Here's a route generally on low-traffic roads which is not as direct as taking I-10 from El Paso to Casa Grande, but is a lot more interesting and enjoyable than riding the shoulder of the interstate. West of El Paso, ride NM Highway 9 all the way across southern NM. That road is scenic and very lightly-traveled, and the towns (Columbus, Hachita, and Animas) range from small to tiny. At the Arizon border, take Highway 80 through Douglas, Bisbee, and (for the atmosphere and history) Tombstone. Take Charleston Road from Tombstone to Sierra Vista; Highway 90 and Highway 83 to Sonoita; and Highway 83 to I-10 east of Tucson. Shortly thereafter, frontage roads lead into Tucson. Bicycles are prohibited on I-10 from the east side to Tucson north thrugh Casa Grande to north of Phoenix.
You can get a bike route map of Tucson which shows bike paths and routes through most of the city. Take Oracle Road (Highway 77) north out of Tucson to Highway 79 to Florence, then Highway 287 from Florence to Casa Grande. Then take Highway 238 to Gila Bend. There are frontage roads along much of I-8 west of Gila Bend; where they aren't present, ride the interstate shoulder. At I-8 Exit 54, take the paved road to Tacna, Wellton, etc. to Yuma -- the road avoids a mountain range that I-8 crosses east of Yuma.
This routing from El Paso to Yuma is high desert and desert that get very hot in the summer, with long stretches between water sources and other civilization. I've ridden virtually all of it and it's wonderful riding, but be prepared.
I haven't ridden from Yuma to San Diego, but you could likely find journals on crazyguyonabike.com of that portion. Not too far west of Yuma, you can pick up the Southen Tour route.