Controlling high rating DC motor

You should not use that driver if you think you'll be pulling that much current. For one, it's rated for 3A for a maximum of 10ms per the datasheet and you'll certainly try to draw for longer than 10ms in a stalled condition. And that is the maximum rating for the device which the datasheet says is not to be exceeded under any circumstance. It sounds to me like you'll be abusing the poor thing. Find a beefier driver, or if you're feeling really adventurous, parallel two of them. Is that a good idea? I've never done it, never heard of it being done, and wouldn't do it myself, but you could certainly try :)

I would just find another motor driver on pololu's site. It looks like there's plenty of them. Make sure their maximum CONTINUOUS current is greater than your stall current.

“I assume it [inability to run servo directly from mocrocontroller] has something to do with power.”

You’ve probably answered your own question. Most motors useful for robotics consume more current than a microcontroller pin can source or sink. (Unless, you’re building a micro-miniature robot.) As a result, the motor requires a power driver, such as H-bridge made with power transistors. For an example of an integrated H-bridge driver, see L298 (dual H-bridge) and A3966 (application note).