Why not just take your passport? I crossed from Tijuana to San Diego by car yesterday. My colleague (green card) and I (citizen) were asked for "identification." We handed over our passports and 10 seconds later we were cleared through.

If you do choose to drive, your US insurance may actually cover you in Mexico (mine does). However, I bought Mexican insurance anyway, just in case the US insurance was questioned by the police if I had a problem.