Question

Does the number of steps equal the number of EXP required to level up a Pokemon in the day-care?

Answer 1

http://bulbapedia.bulbagarden.net/wiki/Pokémon_Day_Care

That has all the information you need to know about the Day Care. It says there,
>Pokémon in Day Care gain one experience point per step the player takes.

So basically however many experience points you need to level up equal the amount of steps to take.