Published reports out today have squelched the long-standing rumors that former New York City Mayor Rudy Giuliani will run for governor of New York State. But, what if Giuliani makes a bid for the U.S. Senate? Giuliani leads U.S. Senator Kirsten Gillibrand, the Democrat appointed by Governor David Paterson to fill the vacant seat left by Hillary Clinton. 54% of registered voters statewide would vote for Giuliani compared with 40% who would support Gillibrand. Even one-third of Democrats report they would back the Republican challenger, and Giuliani runs competitively against Gillibrand in overwhelmingly Democratic New York City.