The Spurs will have to improve immensely to get to a championship level. (In fact, they will have to improve considerably just to end up with the fourth seed.) A championship right now definitely looks like a long shot with the way the roster is composed but I think there's a chance.
TP and Manu would need to get healthy, stay healthy and play at very high levels. Duncan will need to avoid the physical letdown he suffered last season in the second half. Then the role players would need to fit in better. RJ would need to find his niche, McDyess would need to defrost and return to his normal level, Hill would need to continue to blossom, Blair would need to keep learning and improving ... and so on down the list.
The good news is that every team out there is beatable. I view the Lakers as far and away the best team in the NBA but they aren't unbeatable. The Spurs would have to play at their best to have a chance but the talent and upside is there.
All that said, reaching a high level might not even be the most challenging part because I think there's a relatively good chance that the Spurs fight through their funk and turn it around. The more challenging aspect will probably be staying at a high level. With as fragile as the Big 3 are right now, it'd take somewhat of a miracle to remain healthy and rested enough to endure an entire playoff run.