In principle, I agree with you. In practice, I don't see how it is politically possible. An amnesty visa for each more desirable (or even least undesirable) illegal alien in return for permanent deportation of the most undesirable illegal aliens is, at least, a partially desirable outcome.
As you say the "advocates" have been playing the game of saying that we should deport the 2 million or so criminal illegal aliens and allow the "good behavior" illegals to stay under certain conditions. You and I both know that a game is all it is. When push comes to shove, nobody gets deported and everybody stays. The vote which I reproduced on the Cornyn amendment makes that crystal clear.
The proponents of amnesty are wont to create the false choice between a blanket amnesty and mass deportation of 12 to 20 million illegal aliens. In reality, we have other choices and alternatives that don’t reward people who have broken our laws with the right to stay and work here and an eventual path to citizenship.
The 12 to 20 million illegal aliens did not enter this country overnight and they will not leave overnight. Attrition through enforcement works. We have empirical data from Georgia, Oklahoma, and Arizona proving that it does. During the 2006 amnesty debate, the Center for Immigration Studies (CIS) commissioned a Zogby poll offering respondents not the false choice between mass deportation or amnesty (a word CIS did not use in the survey), but rather a three-way choice between mass deportation, earned legalization, and attrition — and attrition was preferred two-to-one over legalization.