And sweet talking the Chamber of Commerce and pro-amnesty lobbyists? Maybe, but they might be harder to fool, and the consequences for double crossing them is more difficult to fix.
Before this announcement, John Carter (TX-31, my district, and a member of what was at that time the pro-amnesty House "Gang of 7" but now is smaller without Carter and Johnson, leaving only one GOP member and 4 Dems) was selling amnesty at those groups in person. He also tried it at a Texas Tea Party group this year, but they were not buying, and in fact some members were talking about a primary challenge after that event.
Don't celebrate too soon though. We know what happens in horror movies after they think the monster is dead.