If the bike has appropriate gearing, then you shouldn't have to pedal harder (or more cycles) with smaller wheels.

I have 3 bikes that I ride regularly - a Peter Mooney touring bike with 700c wheels, a Bike Friday Air Glide (set up as a touring bike) with 20 inch (406) wheels, and a Bike Friday Pocket Rocket (set up as a road bike) with 20 inch (451) wheels. The chain rings on the bikes with little wheels are bigger than the chain rings on the bike with "normal" size wheels - my gearing on the two touring bikes is exactly the same. And the gearing on my Pocket Rocket is actually higher than that on the touring bikes.