In Washington, Democrats won the White House and expanded their control of Congress. Albany is run by a Democratic governor, Democratic Assembly leader and a Democratic Senate majority leader. Everywhere New Yorkers look, Democratic dominion is spreading. Except in New York City. The city may be a bastion of American liberalism, where registered Democrats outnumber Republicans nearly six to one, but it can’t win the mayor’s office. Nearly 16 years since Republican Rudy Giuliani ended decades of Democratic control of City Hall, prominent Democrats acknowledge that the party is still debilitated by dependence on special-interest constituencies, political legacies, a resistance to structural reform and an overall absence of new ideas.