Labor officials said the union contributions to the business group in 2011, which were revealed in records filed with the federal Labor Department and interviews with people familiar with the donations, reflected workers’ deep unease about a slowdown in the construction industry in New York and their hope that Mr. Cuomo and the business committee could persuade voters and lawmakers to support publicly financed building projects and encourage growth.

But the unions’ aid to the business coalition also shows how battles over government spending, especially at the state level, have deepened longstanding tensions in the labor movement between union members employed by government and those employed by private business…

One labor official, who spoke on the condition of anonymity to discuss the unions’ decision, said that unlike public workers, union members in the building trades — electricians, construction workers and plumbers — could not qualify for benefits unless there was private sector work to be had.

“We don’t have pension funds if our members are not working,” the official said. “We don’t have health insurance if our workers are not working.”