Teraforming an entire planet would, in many respects, be simpler than safely teraforming just the Sahara and nothing else at the same time.
We don't even need to make Mars better than the Sahara. The primary objective would be to raise the pressure to that at which a pressure suit wouldn't be needed, and the temperature such that that too would meet what we currently can handle on earth. Once we've got that, the rest would be fairly straightforward (I'd argue that atmospheric manipulation is harder than getting life to colonise the regolith).
We don't even need to make Mars better than the Sahara. The primary objective would be to raise the pressure to that at which a pressure suit wouldn't be needed, and the temperature such that that too would meet what we currently can handle on earth. Once we've got that, the rest would be fairly straightforward (I'd argue that atmospheric manipulation is harder than getting life to colonise the regolith).