From what I can tell, Rudy is targeting primarily crossover votes from Democrats and 'base' those who will vote for any candidate with an (R) next to their names. If he gets in, he'll be much more beholden to crossover Democrats than to conservative Republicans.
I was thinking more of votes in Congress.
This brings up another scenario I was considering. Rudy is nominated. A portion of Social conservatives refuse to vote for him in the general election. He gets elected anyway somehow with these crossover voters. He now has even less of an obligation toward soc cons than he would otherwise. The Republican Party shifts more leftward.