I would say that the bigger difference isn’t so much about the leadership style as it is that Cuomo won. Suppose that the New York State Senate operated according to the rules of the United States Senate and a bill failed unless it secured a 60 percent supermajority. What would people be saying about Andrew Cuomo now? Well, it seems to me that many people would be castigating his failed leadership. Instead of Michael Barbaro’s account of his behind-the-scenes leadership reading like a virtuouso performance it would be reading like a story of a failed inside game. The meeting with high-dollar pro-equality Republican donors would seem not savvy, but naive and weak. Conversely, if the US Senate operated on a 50 vote rule, then both the Affordable Care Act and the Dodd-Frank bill would have gone further in advancing progressive priorities, there would have been more economic stimulus in the 111th Congress, the DREAM Act would have passed, and it’s conceivable that some kind of nationwide carbon pricing scheme would be in place.
Which is just to say that political institutions matter, a lot. Getting concurrent majorities in two legislative houses, as Cuomo did, is very hard. Getting a 60 percent supermajority is harder.
None of what I'm saying, btw, is to take anything away from Cuomo or to defend Obama. I'm finding your post a useful jumping-off point for further research, though.
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