Public unions are the focus of intense attacks from Republicans, including the wealthy conservative donors whose millions of dollars helped Gov. Scott Walker defeat a labor-backed recall effort in Wisconsin this week. But as states struggle with declining tax revenues, and as gridlock in Washington leaves little prospect for additional federal aid to states, the alliance among Mr. Cuomo, the Committee to Save New York and the private unions reflects a new level of complexity to labor’s plight. Even as unions face off against Republican opponents, they are also often at war with a prominent Democratic governor, who has conquered Albany in part by dividing labor in the country’s most unionized state.

“I think that any efforts to split the labor movement, whether it’s Democrats or Republicans, are unwelcome and not helpful to long-run stability in the state,” said Michael Podhorzer, the political director for the A.F.L.-C.I.O. “I think that ‘exploit’ is the right word,” he added. “You could see in the Walker recall that the labor movement remained very unified.”

The unions contributing to the Committee to Save New York included the Mason Tenders’ District Council, which oversees local laborers’ unions in New York City, as well as affiliates of the Laborers Eastern Region, an organization of laborers unions in New York City, New Jersey and Delaware. Gary LaBarbera, president of the Building and Construction Trades Council of Greater New York, sits on the committee’s advisory board.

The council joined “because we believed it was important to support the governor’s agenda of bringing fiscal responsibility to New York and attracting private investment and job creation to our state,” said Paul Fernandes, a spokesman for Mr. LaBarbera.

“It should come as no surprise,” he continued, “that we would want to work with other civic and business leaders to support efforts to get our state on sound fiscal and economic footing.”