We haven't lost that many lives. Not compared to Iraq. And not by any standard. Also, we've been fighting the Special Republican Guard. Not the Elite (yet).
The Elite Republican Guard isn't the problem. They are tough. But we are the elite of the elite. We can take care of them. The problem is that Iraq will use thousands of civilians as shields and will hide behind them. They will scatter them and do anything they can to make it look like we target civilians.
That's the only hope Iraq has and has always relied upon: Public perception/opinion.