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“The governor’s re-election success has been on his ability to keep a lid on state spending and state taxes,” Mr. McLaughlin said. “In New York City it is pretty clear that de Blasio wants to raise income tax on job creators and probably will create a spending situation where he will have to raise other taxes, which is exactly the opposite of what Cuomo has been trying to do.”

Mr. McLaughlin said this difference between the two men “is going to create major cross pressure from the governor, who is trying to win re-election on a fiscal conservative and socially moderate platform.”

Larry J. Sabato, head of the University of Virginia’s Center for Politics, said that Mr. de Blasio could reinforce the party’s liberal wing heading into the 2016 presidential primaries and fuel a Democratic presidential candidate who will run from the left, suggesting that candidate could be Mrs. Warren, Mr. Dean or former Montana Gov. Brian Schweitzer.

“Of course, there are a lot of big ‘ifs’ there,” he said. “Will those candidates actually run? And, most important, will de Blasio be successful or just controversial?”