The first step already breaks our $3/day budget, but I don't see a way around it. The highway 17 express from downtown San Jose to Santa Cruz is $4.00 one way. Santa Cruz is a nice town, hang out and enjoy it, because from here on down the coast it's a hell of an adventure.
Santa Cruz to Watsonville is the next transit-traversible route. Take the number 71 bus for $1.50. From there? Well, it's up to you. This is the 150 miles I mentioned, from Watsonville to San Luis Obispo. There are more buses south from there, for $1.75 each, heading down highway 1 or east over to 101, but they won't take you more than 30 miles of the way or so, and with 3 legs of the journey no matter which way you go, that's an expensive 30 miles at $5.25. I chose instead to strike out on foot down highway 1 and hitchhiked, and made it to San Luis Obispo in less than 24 hours thanks to 3 rides. Details at my blog.
From San Luis Obispo to Santa Maria there's a bus, route 10.
From Santa Maria to downtown Santa Barbara is still a long way, and there is no daily public transit that I could find. There are some once-a-week buses that go parts of the way in either direction, but there is one daily resource that I intend to try next time I go: the Chumash Casino shuttle. Pick it up in Santa Maria, drop a few bucks into the slots, then take the shuttle to Santa Barbara. Will they let you do that? No clue. Maybe they will only take you back the same way you came. And how much you want to pay (by gambling) is up to your conscience, unless they have some way of tracking that (I doubt it).