Supervisor Ally Miller has proposed not replacing deputies who have have quit or retired. The Sheriff’s Department has 151 positions vacant.

The Pima County Board of Supervisors failed to come to an agreement on a $1.4 billion budget Tuesday after a last-minute proposal to temporarily institute a hiring freeze that would include new sheriff’s deputies.

The last-minute proposal by Supervisor Ally Miller is an attempting to cut at least $10.6 million from the budget to avoid raising property taxes.

Miller’s proposal would delay the planned hiring of at least 1,000 employees for two months. She says it would save the county about $4.1 million dollars. Her plan includes not replacing deputies who have have either quit or retired.

It was unclear Tuesday how her proposal would affect county services.

Supervisor Richard Elías said he had little interest in evaluating Miller’s latest proposal, saying a freeze would hurt the county’s ability to deliver services, especially those related to law enforcement.

The Pima County Sheriff’s Department has 151 positions that are vacant, although that includes various unfilled administrative posts, not just deputies.

“It further limits us on being able to provide the services we are supposed to provide to people,” Elías said.

Elías said smaller departments in the county would struggle to operate if key positions are left empty for months.

“Our employees have been ridden very hard over the last 10 years due to our inability to fund things appropriately,” said Elías, a Democrat.

Miller, a Republican, also floated a secondary proposal to delay the hiring of just 500 employees for at least four months, allowing county departments to prioritize hiring over the next fiscal cycle.

Miller concedes the proposal needs to be vetted by County Administrator Chuck Huckelberry and voted Tuesday morning with a majority of her colleagues for a two-week delay on a formal budget vote.

Miller, who has previously proposed spending cuts, says her goal is to cut $10.4 million out of the proposed county budget to avoid raising property taxes .

Huckelberry poured cold water on an across-the-board hiring freeze during Tuesday’s meeting, saying such plans are difficult to implement.

Elías was the lone holdout to delay the budget vote, saying the freeze would harm county services, including public safety.

The vote on the county budget is now set to be held July 2.

Contact reporter Joe Ferguson at jferguson@tucson.com or 573-4197. On Twitter: @JoeFerguson