With the city's hotels in the midst of a sudden slowdown in business, operators are seeking wage cuts and other concessions from the unions representing 27,500 bellhops, housekeepers and waiters. But the unions are drawing a line across hotel lobbies, from the high-end Carlyle to the more budget-minded Ramada Inn, saying they see no need to bend now that operators are cutting rates in an effort to fill vacant rooms with tourists, executives and other travelers. It is far too soon to judge the financial health of the industry, said Peter Ward, president of the New York Hotel and Motel Trades Council, an alliance of hotel unions.