Woah, back up a bit, you are doing the classic thing, confusing amp hours with amps. The controller, or the motor, does not care about the ah. that's just the size of the gas tank. The controller does control the amps, but it does not care how much amps the battery can supply. Too high a volts can damage a controller, for example a 48v controller can't be run on 72v.
However, you might have a big enough tank, to run long enough, to overheat a very small motor if you are riding up steep enough hills, or weigh a lot. This is what the others are talking about.
But under reasonable conditions, your motor and controller can run infinitely, not caring that the ride may be 3x longer than a typical ride. What's reasonable? That varies depending on the motor, your weight, the grades of the hills, and the weather. So we need a lot more info to say if you can ride your bike everywhere all the time, or just some of the roads in your area, when the weather is good.
