I think he's also afraid of a confrontation at the border when we try to return busloads of illegals which Vicente Fox doesn't wany - any more than any of the various muslim nations want the "palestinians". I believe the Mexican government will order their troops to fire on those buses and, if we don't have the courage to persist, we'll end up with some kind of permanent "resettlement camps" along the border.
President Bush is also afraid of the "heads I win - tails you lose" response from Democrats who will announce that whatever solution he utilizes to solve this very real problem is "wrong-headed, immoral and lacking 'nuance' of the gray areas". Add to that the heart-wrenching stories you'll see on TV about Jose and Maria who were once "living the American dream" only to be snatched up to be used as "political pawns" in some evil right wing border war and you've got a witches' brew which, I'm afraid, America doesn't have the will to resist.
I am fully in favor of the government deporting every illegal it happens to encounter. But I do not advocate mass sweeps, roundups and deportations and neither do most others who have given this problem serious thought. For all the reasons you stated, that solution will never fly. And why should Americans should be taxed for that cost which Chertoff has correctly estimated to be billions of dollars?
Instead, we need rigorous workplace enforcement and we need to cutoff all access of illegals to social services (except emergency medical care). When the jobs and the benefits dry-up, they will slowly self-deport the same way they came: on their own two feet and at their own expense. It took years for the problem to get this bad and it will take years to solve it. The key is to reverse the flow.