A hunger strike by eight janitors at the University of Miami is entering its 10th day with no signs of a breakthrough in the standoff between the workers, who are seeking union recognition, and the former Clinton administration official who serves as president of the university, Donna Shalala.

The heated labor dispute involving Ms. Shalala, a former health and human services secretary considered one of the most liberal members of President Clinton’s Cabinet, has drawn the intervention of several high-ranking Democratic politicians, including a former senator from North Carolina who was the party’s most recent nominee for vice president, John Edwards.

“I work hard and I feel my work is not being compensated and we’re not being respected,” one of the cleaning workers on the hunger strike, Clara Vargas, said in a conference call organized by the Service Employees International Union.

At least three workers have left the hunger strike and been hospitalized. One worker suffered a mild stroke, union officials said.

“I’m feeling weak and my son is worried about it,” Ms. Vargas, a Cuban immigrant who spoke through an interpreter provided by the union, said.

The president of the SEIU, Andrew Stern, was grim about the hunger strike, saying, “It appears to only have a tragic end in sight.”

Mr. Stern said he laid blame for the impasse squarely on Ms. Shalala. “Ironically, the very person who holds the, quote, health and human safety of these workers in the palm of their hands is Donna Shalala,” he said. “At any time she chooses, it can be over.”

In response to student pressure and a work stoppage that began March 1, the Coral Gables, Fla.-based university recently announced substantial wage hikes for employees like Ms. Vargas, one of about 425 janitors employed through a national cleaning contractor, Unicco Service Company. Pay for cleaning staff was raised to about $8.55 an hour from near the state’s minimum of $6.40. The school also rolled out a program to help low-wage workers pay for health insurance.

Despite the pay concessions, the labor dispute has continued, with the workers and the company at odds over the method to be used to decide on union representation.

The Service Employees’ favor a “card check” in which signed statements of support from affected employees are gathered and submitted to an auditor to determine if more than half of the staff has endorsed the union. The company, Unicco, has said it wants a traditional election under which potential union members vote by secret ballot.

Ms. Shalala did not respond to an interview request, but a vice president of the university, Sergio Gonzalez, said the issue of how to decide on union representation “is between the contractor and the workers.” However, he suggested that the university views the ballot method as more democratic. “They’re asking us to intercede and do away with a democratic, confidential vote,” he said.

An organizer for the Service Employees, Renee Asher, said unions prefer the card-check system because employers often challenge elections before the National Labor Relations Board, leading to delays in recognition that can stretch for years. “NLRB elections provide the employer with a bunch of different opportunities to scuttle the process,” she said.

Ms. Asher asserted that 90% of Unicco’s union work force achieved recognition through card check, but a spokesman for the Newton, Mass.- based company, Douglas Bailey, said the correct figure was “maybe about half.”

Mr. Bailey said the company agrees to card checks where elections would be expensive because of the number of employees involved or where majority support for the union is clear. He said neither condition applies to the workers at the university.

“The strike has only gathered support from 25% of the workers,” Mr. Bailey said. “They’re essentially asking us to put people in the union who have told us they don’t want to have a union. If they thought they’d win an election, they’d be banging down our doors to have an election.”

Union officials said they don’t trust the company to keep its promises about an election, in part because of alleged labor law violations. Federal regulators have found probable cause to conduct a trial on the charges, which the company denies.

Asked about the hunger strike, Mr. Bailey said, “It’s unconscionable. The idea that we should make decisions based on how long five people can go without food is unbelievable.”

On his blog, the spokesman suggested the hunger strikers were cheating by eating fruits and vegetables. “Hmm, that’s what we used to call a diet,” Mr. Bailey joked. He later said the statement was directed only at students who purported to join the hunger strikers but have been eating some foods.

A spokesman for Mr. Edwards, Kim Rubey, confirmed that the possible 2008 presidential hopeful is supporting the unionization effort, but said his efforts to reach Ms. Shalala to discuss the standoff were unsuccessful.