New York Gov. Andrew Cuomo has studiously avoided talk of a 2016 White House run, but he has positioned himself on two fronts, amassing the nation's largest gubernatorial war chest and organizing a series of August policy summits with Democratic leaders and academics.

Mr. Cuomo has raised nearly $1 million a month since he took office in January 2011 and has about $19.3 million to spend—more than 40 other governors combined, according to a Wall Street Journal analysis of campaign finance data in 50 states.

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