Outstand answers, thanks guys! I tried the CLR and indeed, almost no effect. I'll try the Wink rust remover next. Yes, probably not in the tank as that may damage some of the float/levers
CLR works very slowly. The phosphoric acid in it dissolves rust slowly, though safely. That's why it works well in coffee makers, though it might take days of soaking to make a difference in this toilet.
Ospho is the metal paint prep chemical that's a stronger phosphoric acid, plus a detergent. It would give similar results. It might work well if allowed to soak over a weekend. Either of these will work better if hot.
Bar Keeper's Friend uses oxalic acid. It converts rust into a clear soluble form, but works best with some frictional help. I really prefer the powder to the liquid, as I can mix just a few drops of water with a bunch of powder to form a thicker paste that works better. If you're going for the elbow grease solution, this would be it, and as I said above, pumice will help greatly. Pumice sticks:
http://www.homedepot.com/p/Pumie-Scouring-Stick-HDW-12T/202529733?keyword=pumice+stick
are made for just this. They will NOT scratch porcelain, and are amazing at cleaning toilets, if you really feel like gloving up and reaching in there. They're also amazing on ceramic stove tops (although they are not safe on the glass control panels), though I'd suggest buying separate sticks for each task.
Muriatic acid will dissolve the rust VERY quickly. Though I would not suggest this route without serious caution and preparation (including splash proof face protection). It will bubble and splash, the tiniest droplets will burn holes in your clothing (or skin), and the fumes within the bowl could easily reach deadly proportions.
Last on this list is Whink rust remover. I'd seriously suggest using muriatic acid (aka pool acid or hydrochloric acid) before using this. I just looked up the MSDS on it, and the active ingredient is hydrofluoric acid. Forgetting for the moment the effects of even dilute HF on the human body, let's just focus on the toilet. Yes, HF will rapidly dissolve the rust, but it will also etch the porcelain, leaving it more vulnerable to future "rusting". Just imagine suggesting using a sandblaster to remove bird poop from your vehicle's paint.