I don't know the answer, but start here:
Looks like 1 1/4 is 32 mm.
1 1/8 is 28.
1 is 25.
... ah, there's a note on the tire choices at Harris Cyclery. They show rims with widths of 22 and 19.5. They say that these rims will work with any 27" tire. Supposing that your bike now has rims sized for 27X1 1/4 (and the widths of the tires above correspond to the OUTSIDE width of the two 27" rims sold by Harris), that could mean you'd be safe with tires of width /about/ 28-47. Pretty wide range. So you could probably surely go with 1 1/8 tires. This is just my reasoning. I always go for the fat boys. I would never ride skinny little bone rattling, urethra crushing little tires like that.
It might be that there's total compatibility across 27" sizes. It would help if Harris gave nominal width names for the 27" rims they sell.
Hopefully someone more knowledgeable than me comes along.
Last edited by Roll-Monroe-Co; 06-20-10 at 02:23 PM.