David Spatafore, an agency lobbyist, said lawmakers will relent once they're satisfied UCA is back on track.
"They see the need for funding," he said in an interview.
UCA and its lawyers have blamed a decadelong embezzlement on former administrative assistant Patricia Nelson and her daughter, Crystal Evans, who signed a confession in a $2.3 million civil judgment.
West Valley City police are conducting a criminal investigation with assistance from the FBI and Salt Lake County district attorney's office.
One of the items on the legislative checklist for the agency is to hire a new director to replace Steven Proctor, who resigned in the wake of the scandal, though he has not been implicated in wrongdoing.
Board member Dean Cox, who sits on the agency's recruitment committee, said UCA hopes to narrow a search to three finalists for the directorship by the end of June.
While Mathieu told lawmakers last week that UCA is working to comply with all recommendations in the audit, she and other board members have expressed concern at one: that the 27-board member is too unwieldy and may need to be scaled back. The agency employs 24 staff members.
Board member Rick Bailey said the board needs to keep its size to ensure that all stakeholders have representation.
Mathieu suggested creating an executive board of five or six people.
"If we don't create an executive committee, I'm pretty sure the Legislature will reduce our board," she said.
Cox supported the idea, while board member Jason Davis said he is concerned that this step wouldn't be enough to appease lawmakers.
Mathieu said she didn't think it would be a problem, as long the agency shows it is addressing the main issues pointed out in the state audit. The Legislature has ordered its own far-reaching audit, which is not expected to be completed until September.
"The next six months will tell us a lot," Mathieu said. The board has begun to comply with many of the state audit recommendations, including replacing agency credit cards for state purchasing cards and complying with state transparency laws.
Among other problems, the audit found the UCA board had repeatedly violated the Utah Open and Public Meetings Act.
It was a different story Tuesday, when the body announced the reasons for going into closed session, took a roll-call vote, and then, once the session was reopened, made a clearly stated motion and voting by roll call.
After about 30 minutes in executive session, the board unanimously approved a motion to grant its outside law firm authority to retain a forensic accounting firm to work in concert with criminal investigators looking into the embezzlement.