The bosch/sabatier reactor? It's actually well tested. And the atmosphere is over 90% CO2 if I'm not mistaken. All you need to bring with is hydrogen. As for water ice, there's plenty of it near the surface in some areas. I don't see what is impossible to do here.
Mars has a little over 95% CO2 in it's atmosphere so yes, plenty to go around. We could also get additional hydrogen from extracted water ice. Wiki mentions another option with the Sabatier process, producing excess methane can be used to extract more carbon and hydrogen which then can be recycled back into the reactor.
"Since we first emerged, a few million years ago in East Africa, we have meandered our way around the planet. There are now people on every continent and the remotest islands, from pole to pole, from Mount Everest to the Dead Sea, on the ocean bottoms and even, occasionally, in residence 200 miles up - humans, like the gods of old, living in the sky."