The problem with "Hey, now we'll just support immigration reform!" is that the people voting in the GOP primaries will still include the same xenophobic, "English as national language", "immigrating illegally is the same as being an axe murderer or rapist", "anchor babies are future terrorists", "dirty lazy brown people took my jobs", "Build a giant border wall with barbed wire and machine guns" voters it contains right now.
The GOP can claim whatever they want as a platform. Ultimately it's the base that decides what the party will run on.