“With a Republican Congress,” Mr. Stringer said, “if their rhetoric creates actionable items, we could potentially constrict or collapse the safety net in the city and that is a very real threat to the survival of a lot of vulnerable New Yorkers.”

Eric F. Phillips, Mr. de Blasio’s press secretary, said city lawyers and budget officials were preparing what he called an “exposure sheet,” highlighting programs that may be most vulnerable.

Though city officials had promised to provide details of their work, they reversed course abruptly this week and refused to offer additional information.

“The legal and financial analysis of our potential exposure is not yet complete,” Mr. Phillips said in an email.

Estimates vary as to how much money the city receives from the federal government, but a study by the city’s Independent Budget Office put the total last year at about $7 billion. A review by Mr. Stringer’s office estimated the amount for the current fiscal year, which began on July 1, at somewhat higher than that, though less than 9 percent of the city’s overall budget, excluding recovery aid related to Hurricane Sandy.

Mr. Shorris said that concerns went beyond direct federal financing of city programs.

One threat is connected to Republican vows to repeal or weaken the Affordable Care Act. If that happened and large numbers of city residents lost their health insurance as a result, they would most likely seek care in city-run hospitals. That would greatly increase the burden on those hospitals, the largest provider of care to uninsured New Yorkers.

Legal precedent may require that any cuts to federal funding be related to an issue in dispute between the city and the federal government. If, for instance, the city refused to allow the Police Department to cooperate with deportation raids, it could put money tied to the criminal justice system at risk.