Your Schwinn American is probably a middleweight, which took 26 x 1 3/4" (571x45mm) tires. You're not going to get 3.1" tires in there without frame mods. I've run some balloon tires (26x2.125"/559x55mm) on Schwinn middleweights, pretty easy. You'll want to measure how much room you have between the chainstays about 11" from where the axle sits in the dropout (remember, middleweight Schwinn wheels are s7-sized, and actually larger diameter at the rim); you'll need an 1/8 to 1/4"of clearance on each side, so allow an extra 1/4 to 1/2". Also keep in mind that, if you want to run fatter rubber, you'll have to change the rims, b/c 99.9% of s7 tires are 1 3/4". As for the repop springer, that should easily run balloon tires (26x2.125") and probably fatter; same deal: measure about 11" from the axle, both up-and-down and side-to-side, to see what you can fit....
HTH
Rob