CHICAGO (CBS) — Hyatt hotel workers rallied outside company headquarters downtown Wednesday to protest what they see as threats to cut off health care.

But as WBBM Newsradio’s John Cody reports, the hotel chain says the union is not playing fair.

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LISTEN: WBBM Newsradio’s John Cody reports

Members of UNITE HERE Local 1 protested in front of the company headquarters at 71 W. Wacker Dr. They say Hyatt has told them health care will be cut off in 60 days unless union members call off a boycott and settle the 28-month labor dispute.

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“Me myself, I have heart problems and I have high blood pressure,” said Jaclyn Smith, a 10-year veteran room attendant for the McCormick Place Hyatt. “If I don’t get my medication, or they take away my breathing machine, then I can’t support my family, because I am the sole provider for my family.”

But Hyatt Regency Chicago general manager Patrick Donnelly says the union is not telling the whole story, which includes a national union agenda.

“The union would like us to give them four hotels in other cities – non-union cities – right now, with card-check neutrality, and we say that every employee has a fundamental right to decide whether they’d like to be union or non-union,” he said.

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Asked if the hotel is threatening workers with a health care cut off in 60 days, Donnelly says he hopes there’ll be a settlement before then.