IMO, we could be there tomorrow with significant risk.
I've thought the military strategy all along was to push inwards to develop a ring around Baghdad and then wait it out. We assure ourselves of eliminating outside threats, reduce risk of missile attacks on Kuwait and Israel, provide positive humanitarian efforts where secure, get Iraqi people on our side and then let Baghdad stew...
Part of the reason we've kept infrastructure in place, IMO to get news of "liberated" cities into Baghdad....
...then again...what the hell do I know.
That is absolutely the way to go. These forces can be greatly attrited through the air. Let the "irregulars" and the Fedayeen come in and die at the feet of our soldiers. Time is on our side. By the time we actually go into Baghdad, there will be nearly nobody left to stop us.