The problem is that Bush's entire public premise is that his proposal is compassionate without rewarding people for breaking the law. Yes it's a dog and pony act, but he's been selling tickets for years and many have paid the price of admission.
Your compromise would entail a lesser, but possibly more obvious reward to illegal aliens. Bush's best shot, from his perspective, will be to maintain the charade and try to strong arm this thing. He's got a big hurdle getting it past Sensenbrenner in Judiciary, not to mention Tancredo's 70+ votes and Hastert's reluctance to do and end around of his own caucus.
Bush might back down, but he's been girding himself for this fight for five years, so it will require a bitter fight and defeat for him to do so. I hope I'm wrong, because I think David Frum is right.