However, the wording of much of this polling does not describe the president's/the Senate's plan accurately. The wording of the poll questions is often something like the following:
Would you support legislation that would significantly increase border security, block employers from hiring undocumented immigrants, and make sure that undocumented immigrants already in the U.S. with no criminal record register for legal status? If immigrants were to meet a list of requirements, they could eventually apply for citizenship.This wording heavily emphasizes enforcement---which could easily be gutted. Moreover, it makes no mention of a huge expansion of guest-worker plans, a central piece of the Senate bill and reportedly under consideration as part of the Speaker's immigration "principles." Also, under the Senate bill, illegal immigrants who have been convicted of multiple crimes could still receive legal status.
GOP House members might be wary about listening to the advice of this memo.
UPDATE: A memo from Senator Jeff Sessions's office has some more info on polling.