The Shepherd Pass trailhead requires a high-clearance (if not 4wd) vehicle.
When I was up there in September the road to the hiker TH was in good shape. No high clearance needed. There were many small subcompact cars with about as much ground clearance as a skateboard parked. There were a few bigger rocks here and there but if you go slow and know how to drive around the rocks you'll have no problem.
Climbing the Shepherd Pass route is just a suffer-fest that will certainly get you into AMS-ville sooner.
Shepherds Pass, while not my favorite trail by any means (it is a big suck fest with the elevation gain and then loss only to have to regain it) is the quickest way up the Tyndall-Willi area. I broke it up by starting later in the afternoon when things had cooled down and hiking up to Mahogany Flat and camping there for the first night. Second day was up to the pass and saddle between Tyndall and Polychrome. My hiking partner and myself had no AMS related woes on this trip.