Great question. Based on the books that have been written by the current authorities on U.S. straw bale construction (Bill & Athena Steen, Catherine Wanek, etc.) the answer is...
It depends on:
(a) Whether or not you are willing --and able-- to do much of the work yourself (being a skilled carpenter or at least having some building experience is a big plus). Skilled labor is, on average, the #1 cost of building most homes, so whatever you can do yourself = savings.
(b) Where you build (raw undeveloped lots in much of the East Bay is neither plentiful nor particularly cheap --#2 cost on average (however in some cities it can even be #1). Also, building near a fault line, on a steep slope, or otherwise difficult topography adds to cost and engineering challenges. Is it on an already subdivided urban/suburban lot or rural land? Are there utility feeder lines already in place? Access roads or easements?
(c) How elaborate/custom is your design? Things like multiple stories, complicated roofs and architectural features (dormers, turrets), complex building shapes (retangular = easiest/cheapest to build), and custom fixtures/furnishings can all raise the price and engineering complexity dramatically. If you keep it simple, and mainly use recycled/donated hardware and fixtures, that can bring costs down.
(d) Time frame flexibility. If you can live on site during construction (RV, yurt, etc.) and can be flexible on time, that helps immensely and buys you a lot more options. Volunteer labor (family/friends, CASBA) rarely runs on a set schedule, and even professional contractors can often be more flexible on price if you can be flexible on time.
All that said, I've seen some very simple DIY jobs done for as little as $22/sft, while some very custom/luxury contractor built houses cost $200/sft. I personally joined a CASBA plaster party for a San Diego area house several years back that ended up costing around $100/sft as I recall. Of course that was before the real estate bubble imploded, so skilled labor costs and material costs could be significantly lower now.