Would a .22 birdshot be sufficient enough to hunt dove, quail, pheasant? I'm new to hunting and I was just wondering.

NO not enough shot, I am not saying you would never kill a dove or a quail, but I would not give you very good odds. I dont think you could kill a pheasant unless it was a direct shot in the head from very close. I tried shooting a coon with bird shot when I was about 12, 3 shots in the head and all I did was blind him.
I see you are from Illinois, I am pretty sure it is illegal to hunt birds with a rifle regardless of what shot you have in it.

If money is the issue you can buy a New England single shot in 20 or 12 from walmart for a little over $100 bucks.

First of all, it's called rat shot, not bird shot. Second, no, don't try to dove, quail, and especially pheasant hunt with it. I can promise you, it's probably illegal in every state to hunt these birds with a rifle. Rat shot doesn't have a very effective range. You could probably kill one if it were on the ground very close. Why would you even consider hunting with rat shot, other than rats?

Depending on what part of the country you live in it is called birdshot, ratshot, snakeshot.

On most all boxes I have seen it is called "#12 birdshot"

Alright guys thanks for the heads up!

Go get yourself a singleshot 12 gauge. That and a 22. You're ready for any game you'll find in Illinios.