I usually agree with you, but not on this one. Start deporting'em as fast as possible. Maybe we WON'T be able to actually deport them all, but actively working the deportation process will send a signal to those comtemplating illegal entry that the barriers are now up, and it's no longer "business as usual" on the illegal entry front.
ANY other solution involving "amnesty" of any sort simply tells those contemplating entry to "come on down" and if you succeed in entering illegally, then there won't be any real consequences for your action.
It's a free for all now.
There will be reform but it is impossible to roll back the clock of the wink and nod of last decades.