At a glance, an important provision appears to be missing the Senate proposal.
Many who are now in the US illegally will likely fall on to public assistance roles once eligible. Also, many would likely voluntarily deport given the resources and might even prefer to do so. A provision to provide enough money to travel back home and maybe enough to subsist there for a few months could work.
Instead of a “stick” to stay in the US, why not a “carrot” to leave?