PHOENIX -- Could you stop eating for one week? The Maricopa Citizens for Safety and Accountability said it would fast for five days to end what its members call abuses by Maricopa County Sheriff Joe Arpaio.

The fast falls during the weeklong celebration of Cesar Chavez's birthday.

Sunday people packed into the Santa Rita hall in Phoenix. The room is symbolic because decades ago it's where Cesar Chavez fasted for more than 20 days.

Back then, Chavez and others stood up to the Arizona legislature, but this time around the group said its fight is against the sheriff.

"This is not an immigration issue," said organizer Raquel Teran. "It's an issue about safety and accountability."

Teran said Arpaio has not done his job.

"We have 40,000 felony warrants pending, we have more than $42 million in illegal payouts," she said.

One of the fasters, Corinne Widmer, stopped eating Sunday and said she would only drink water until Friday at sundown.

"I know what I'm doing is going to bring justice to Maricopa County," she said.

The sheriff's office said it didn't know about the week of fasting and action until CBS 5 News told them.

Arpaio's office issued this statement reading, "If they want to starve, I'm not going to stop them."

But Celia Arambula, who spent many hours with Chavez, said she believes Arpaio is exploiting the fear some people may have.

"If we do our work and we organize and do what we're suppose to do, he'll get the message that this nonsense has to stop," Arambula said.

She said if Chavez was alive today she knows exactly what he would say.

"Hold politicians accountable," she said. "They must be accountable to the people."

The group said demonstrations are planned around the county this week.