Remember, it's the "special" part that's key here. No brand new green card category that will guarantee everyone a path to citizenship. Instead, you file under existing family and employment-based categories. Here's what Chaiman Goodlatte had to say on Telemundo (as reported in Politico):
“I have always said that if we get border security, interior enforcement, e-verify entry-exit visa systems that deal with the fact that we do not want to make the mistakes made in 1986, and that we can be assured that there will not be continued massive illegal immigration, that we should consider finding the appropriate legal status,” Goodlatte said. He emphasized that he does not support the “special pathway to citizenship” that is part of the Senate immigration bill passed earlier this month.

The big question would then become how do you absorb all of these folks who would overwhelm the very small green card quotas currently available. If we stick with the current quotas set way back in 1990 or don't modify the counting methods to work better (such as not counting kids and spouses in the quotas for green cards - something we already do for the temporary work visa categories), then we'll have backlogs extending out for decades.