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The news on a federal level was no better. Democrats claimed victory over three Republican House incumbents, including Representative Dan Donovan of Staten Island, leaving New York City without a single Republican representative. All told, 21 of the state’s 27 House members will be Democrats, as are both of its senators. (Senator Kirsten Gillibrand easily won her second full term on Election Day.) And one of the six Republican House members — Chris Collins of the Buffalo area — is under federal indictment.

Such a wipeout, and the prospect of a long stay in the political wilderness, has left Republican loyalists trying to find a way forward and the state party chairman, Edward F. Cox, trying to explain his, and his party’s, dismal performance.

“It was a bigger wave than anyone expected,” Mr. Cox said in an interview last week. “There were red swaths across the state. But in the suburbs and the city, we really got hit.”

Indeed, the state’s electoral schism looks much like that of the nation as a whole, with every urban and many suburban areas solidly blue, and rural districts a deep red. But the math of that divide is bad for the Republicans: Residents of New York City, for example, which is overwhelmingly Democratic, make up about 40 percent of the state’s voters, spelling almost certain doom for Republicans running statewide in any year in which Democrats turn out.

That geographic split also prompted questions about whether the leader of Albany’s upper chamber, Senator John J. Flanagan of Long Island, could maintain his position amid calls for new leadership from upstate members and support for Senator Catharine M. Young, from western New York.