SACRAMENTO — A Republican-backed proposal to audit the state Department of Motor Vehicles to investigate the reasons for its customer-service meltdown died Wednesday when three Democratic senators did not vote.

Sens. Jim Beall of San Jose, Ben Allen of Santa Monica and Ricardo Lara of Bell Gardens (Los Angeles County) all declined to vote during a meeting of a legislative audit committee made up of senators and Assembly members. The proposal to audit the DMV needed four yes votes from members of each chamber. Six Assembly members voted for it — three Democrats and three Republicans — but the audit fell one vote short among senators.

“I’m indescribably disappointed by this rank political decision on display,” said Assemblyman Jim Patterson, R-Fresno, who asked for the audit along with fellow GOP Assemblyman Phillip Chen of Brea (Orange County).

The audit would have looked at the accuracy of wait times listed on the DMV’s website and how the agency has spent millions in additional funding the state gave the department to reduce long lines.

State Auditor Elaine Howle told lawmakers that such a review could help explain why millions of people trying to obtain or renew driver’s licenses, including the new Real ID cards, are having to wait weeks for an appointment and then for hours to see a clerk at DMV offices.

“We would put a team on this audit right away,” Howle told lawmakers Wednesday, adding that she does not take a position on whether the legislative committee should request an audit.

Beall, Lara and Allen were all at the hearing, but declined to vote. Lara said the DMV is already overburdened by legislative mandates, and Beall said launching an audit would slow the DMV’s efforts to fix its problems.

“An audit would take seven months, and we don’t want to wait that long,” Beall said in a statement. “The governor has made commitments that he would reduce wait times now. (DMV Director Jean) Shiomoto said wait times would improve by the end of the year. If progress is not being made, I plan to hold her accountable.”

Allen said Gov. Jerry Brown’s office had raised concerns about the audit proposal. Brown’s spokesman Evan Westrup declined to elaborate on what those concerns were.

“We’re throwing everything at this that we can, and look forward to the Legislature approving more DMV staff as quickly as possible,” Westrup said.

Allen said Shiomoto had been “raked over the coals pretty thoroughly” at another legislative hearing Tuesday. He said that hearing identified issues at the DMV that an audit might uncover, and that steps are already being taken to address those.

Shiomoto said Tuesday that an audit would slow the DMV’s ability to reduce wait times, a contention that angered Patterson.

“You should have that information in front of you now,” Patterson said. “An audit is merely going to ask you to divulge and disclose and report.”

Republican gubernatorial candidate John Cox added, “Every hour in line at the DMV is time away from a job or family. Not auditing the DMV in light of blatant mismanagement is exactly why Californians need help.”

The Legislature gave an extra $70 million to the DMV over the past two years to help it meet the demand for Real IDs. People have to apply at a DMV office for the licenses, which they will need to board a domestic airline flight starting in 2020 unless they show federal identification such as a passport.

When Real IDs became available in January, however, the DMV’s customer service collapsed. Appointments are booked up to three months out — at one point this week, no appointments at all were available in the San Francisco office. And even people with appointments have reported waiting for hours, in lines that stretch outside offices, before seeing a clerk.

The $70 million in additional state funding was to ensure the department could add 550 positions and open some offices on Saturdays.

Shiomoto said some offices that added sixth days in January found that few people showed up, so the DMV went back to weekdays only. It redirected the money for Saturday hours to overtime.

The department has been averaging 72,000 overtime hours a month since January at its 172 offices.

Shiomoto, who has headed the agency since 2013, said curtailing the weekend hours was a mistake. Some offices began opening their doors again on Saturdays in June.

“You have my commitment to reduce wait times by the end of the year,” she told legislators.

The Legislature gave final approval Wednesday to a DMV request for an additional $16.6 million to hire 230 staffers for offices with the longest wait times. On Tuesday, Shiomoto said the department needs $26 million on top of that for even more workers — some 400 employees.

Shiomoto said the DMV is updating a four-decade-old technology system whose shortcomings have slowed customer service. She said the DMV has also had to adapt to several changes in state laws in recent years that increased workloads, including issuing licenses for undocumented immigrants and creating a nonbinary gender option on licenses, which will take effect in January.

Lara, one of the senators who did not vote, said lawmakers who are criticizing the DMV should consider their own role in slowing down the department.

“It’s easy to beat up on the DMV and it’s an easy go-to, especially when it’s in vogue in our country nowadays to attack government and discredit it,” Lara said. “But (we should) understand the challenges that the department has had and acknowledge our own responsibility as legislators in terms of lack of funding and lack of support to the DMV.”

The state auditor’s office included the DMV in a recent audit of employees misusing state resources. It found that one DMV worker had slept at least three hours a day on the job for nearly four years. That worker and her manager remain employed with the DMV.

Assemblywoman Catharine Baker, R-San Ramon, said that case showed that the DMV needs more than just money.

“All the training in the world for the culture may be helpful,” Baker said. “But if there is no accountability, it means nothing.”

Melody Gutierrez is a San Francisco Chronicle staff writer. Email: mgutierrez@sfchronicle.com Twitter: @MelodyGutierrez