If you have any water, you can use it in a closed cycle to recycle CO2 by the Sabatier process and partial combustion of the resulting methane into water and carbon. And you'd need tons of plants in any case to feed everyone.
Robotic surface mining might be possible if asteroids are better used elsewhere. It would rely on a lot of ridiculous materials science, but it would be possible.
Apparently it takes something like 100-300 plants (of varying size) to give a person a healthy diet, according to this website.
http://www.wellfedhomestead.com/how-much-should-you-plant-in-your-garden-to-provide-a-years-worth-of-food This is very interesting. So yeah it looks like if you had the gardens to feed 10,000 people (I like Gig's number) then you'd end up with something like:
Let's assume that
each leaf produces 5 milliliters of oxygen per hour, each plant has at least 25 leaves, you need 200 plants to feed someone, there are 10,000 people to feed, and a person consumes 50 liters of oxygen per hour.
(200 * 25) * 10,000) / 1000 = 50,000 liters of oxygen per hour
That's enough delicious oxygen to support 1000 people, or a tenth of your total population. That's pretty good. There are too many assumptions for this to be a scholarly estimate but surely the plants would be supporting at least some number of people which is better than nothing.
The main difficulty of robotic surface mining, I would say, is flying the vehicles down to the surface and back up to the colony. I'm still not totally sold on the idea of floating all of your facilities. Foundries, factories, living areas, agriculture, vehicle bays. At least disposing of waste would be as simple as throwing it outside.
Earlier on in the colonisation process, they could rely on imported dna to help expand their population.
I like that idea. Trading DNA in cold storage for a few thousand adult humans would save
loads of money.