That bottle of CLR that roastbeef posted might actually be a good idea. Only instead of making a dam around the nozzle. Just pour some into the w.washer tank when the tank is nearly empty. Try a 50/50 mix of water and CLR. Then just keep a couple towels on the cowling, winshield or wherevever needed to catch some of the washer mix. Once in the line let it soak for 15 minutes or so or until the nozzle is cleared of calcium deposits. Well.. that is if the nozzel isn't clogged with some other kind of foreign object or debris. If it is, then I guess you're SOL.
P.S. Probably not a good idea to leave the CLR/water mix in the tank for more then a couple hours. Just fill the tank with water...should dilute the mix enough to not be an issue.