Spare tire question

So I recently replaced the 265/70/15 tires with 31x10.5x15 AT tires. I still have the old 265/70/15 tire on my spare. Now I figure there's got be some strain on the axle or differential if I had a flat and had to use the slightly smaller spare tire. My question is just how bad is it, and would I do any damage driving like that for 30 or 40 miles hunting for a tire place. I'll be making a trip from Raleigh, NC to Stanley Idaho in July and I want to make sure they're good for that purpose.

Jim

I wondered the same when buying tires recently and found a discussion here. Just scroll about half way down.

Thanks!!!