The county faces an expected $28 million shortfall in the next fiscal year, and officials are debating how to solve it.
Warren said he has done his part to help the ailing county budget over the past several years by diverting millions of dollars under his control to worker salaries instead of other projects such as digitization.
Improving digital access to documents by computer could reduce a customer’s need to visit the clerk’s office in person.
Now facing this latest shortfall, county commissioners are asking all departments to honor a 90-hiring delay on filling vacant positions.
At Tuesday’s meeting, Warren told commissioners he can’t wait that long for replacements to perform the duties the voters elected him to do under state law.
"I have bent over backwards, three times," he said. "But how many times do I hear, 'Thank you John,' for doing that? Not once."
Commissioner Kenneth Mayfield reminded Warren that commissioners were also elected and their responsibilities include making decisions on Warren's budget.
"Some people think we fund too much," Mayfield said.
Lynn Richardson, an appointed public defender, said she has been forced to serve as the receptionist in her office because of the hiring delays.
"That's not an effective use of my time -- sitting at the front desk -- when I can go down and dispose of cases and get people out of jail," she said.
Commissioner John Wiley Price said the county is pennywise and pound foolish to limit the public defender's budget so much.
"At some point in time, you can't keep driving the attorney who should be in court from doing other work," he said. "That's not what we pay them for."
But Mayfield disputed that claim as well.
"It's not keeping them from doing their job," he said. "Budget has looked at it. For 90 days, they can absorb it."
Commissioners refused to approve a list of requests for travel by county employees that was on the agenda.
"It's like nobody got the message that we have a huge hole in the budget," Commissioner Maurine Dickey said. "I'm very troubled by it."
Two public speakers complained about plans to close the Jackson Street doors at the George Allen Civil Courthouse to save $53,000 on security and metal detector expense. All visitors would use the entrance on Commerce Street instead.
A 3 percent county employee pay cut and a property tax rate increase are among the other county budget options.
A 2-cent increase in the tax rate would cover the entire $28 million shortfall with no further cuts.
In a press release, Dallas County District Attorney Craig Watkins said he could accept pay cuts and furloughs but strongly opposes deeper cuts that would reduce prosecutors or investigators in his office.
"We are already working 68 people short and operating on a budget that is smaller than our neighbors at the Tarrant County DA’s office even though the Dallas County DA’s office handles a larger volume of cases than Tarrant County," he said in the statement.
Price said he is not ready to support a full 2-cent property tax rate increase, but does believe the county budget solution could include a mix of cuts and more revenue.
"I'm not opposed to a tax increase," he said. "Dallas County has the lowest tax rate in the state."
But other members of Commissioners Court were more guarded.
"Right now, a tax increase ought to be off the table," Commissioner Mike Cantrell said. "Every nickel counts, and that's why we’re looking at every single thing that's in the budget."
The county budget debate will continue through the summer. A final spending plan is required by Oct. 1.