The Camino is doable on any bike, if your gearing is too high you will simply need to walk them more.
I started my Eurasia tour by cycling the Camino from Paris to Santiago, and meet folks of all skill levels riding all types of bikes.
I partnered up for over a week with a Croacian woman who was riding what folks in the US might call a "Wallmart bike". She had her gear/clothes in a backpack bungee'd to a seatpost rack. For a good bit of her tour she couldn't use her granny gear (and didn't know it), so she would walk moderate climbs. We spent a good prtion of our ride cycling the walkers route, rather than the road, where walking a touring bike is allmost required at times simply due to the trail.
If you haven't allready, check out the Yahoo group Santiago Bycecleta (spelling is likely a bit wrong-sorry).
Enjoy your tour, it's a great route!