Neither man has definitely stated they will run for governor, but I think they’ll both eventually throw their hat into the ring. Here’s how the early poll numbers look for both men if the gubernatorial race indeed takes place:
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Siena (6/15 – 6/18 with 640 RV’s):
Cuomo 49 (71% view him favorably, and 17% view him unfavorably)
Giuliani 40 (62% view him favorably, and 33% view him unfavorably)
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Quinnipiac (6/16 – 6/21 with 2,477 RV’s):
Cuomo 51 (63% view him favorably, and 15% view him unfavorably)
Giuliani 39 (55% view him favorably, and 36% view him unfavorably)
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Marist (6/23 – 6/25 with 1,003 RV’s): Cuomo 51, Giuliani 43
Cuomo 51 (No data on favorables/unfavorables)
Giuliani 43 (No data on favorables/unfavorables)
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Rasmussen (7/14 – 7/14 with 800 LV’s): Cuomo 48, Giuliani 41
Cuomo 48 (64% view him favorably, and 32% view him unfavorably)
Giuliani 41 (54% view him favorably, and 39% view him unfavorably)
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So, as you can see, Giuliani’s got some work to do. Not only is he lagging behind Cuomo in terms of votes, but he’s also behind in terms of popularity. Both men are popular, but the percentage of New Yorkers who find Giuliani at least somewhat unfavorable is much higher than it is with Cuomo. The former mayor, if he chooses to run, will be fighting an uphill battle, but one that’s not impossible to win.

Giuliani and Cuomo