I've been lurking and occasionally posting on this list for two or three years. Because I like old bikes, I get a lot more schwinns than I do Italian racing bikes, so I know a little. But basically, I'm just replying so I can feel the thrill of giving advice to bigbossman, whom I regard as a central C&V figure and wise, in-crowd cognoscento.
If the bike has the original steel rims, it is stamped with the tire size (i.e., "S-6," which corresponds to one of Schwinn's proprietary(?) tire sizes.). According to the SDLB, the 72 Speedster had Schwinn size 26X1-3/8" tires. I can get these at the LBS. (Actually, I get mine at the local volunteer punk-rock vegan-run bike project, which always has them because 50% of them ride 70s schwinns, and I think we get them through J&B, but I'm not sure.) Any shop that carries Schwinn should still be able to order them. Heck, I recently got a replacement cable for a Positron shifter. So the tires should still be available.
Eric