Differ with you on the last part. It must be an omnibus bill. Otherwise the hard part will not be done.
We need to phase in e-verify  and in the same bill, decide how to deal with the current illegals, how to deal with temp visas running out ( I think e-verify solves that if we require said business to notify us when somebody departs ), and then how to deal with sanctuary gov ( I believe let them go until e-verify fully phased in, then crack down by denying fed money to that gov ).