City Councilman Jack Benson said "two minor details" need to be changed on the new city auditor setup, including one that he says gives the city auditor more job security than "the Pope in Rome."
However, four council members spoke against tinkering with the new system just after voters approved it by a 73 percent margin in the recent election.
The council will vote next Tuesday on whether to make the changes and again submit them to the voters.
Councilman Benson said the term "market rate" is "too broad" concerning the auditor's pay.
He said requiring four of five audit committee members to vote to fire the auditor is too high a standard.
Concerning politics and the auditor, he said during the campaign "yard signs were going up in neighborhoods. I never expected anybody to get out and politick for this."
He said his proposed changes "are like motherhood, apple pie and the American flag."
Councilwoman Sally Robinson agreed, saying the measure "needs a little bit more fine tuning."
And Councilman Peter Murphy said, "It's very good to have independence. It's also good to have accountability."
But Councilwoman Pam Ladd said, "I just don't think it is worthy of the time and money to put it back on the ballot. I think we have enough controls."
Councilman Manny Rico said, "The county auditor makes a lot more than our auditor. Are we going to give him a big raise?" He added, "I want it to be hard to fire the auditor. The idea is to get the politics out. Now you want to get it back in."
Councilwoman Deborah Scott said, "I think we ought to trust the audit committee. The requirements were explained in depth multiple times, and I think it will work well. If not, we can revisit it."
Ms. Ladd agreed, saying, "We discussed this three times ad nauseum each time. The amount of discussion that happened on it was absolutely ridiculous."
Councilwoman Carol Berz noted that "73 percent of the voters approved it. It's disrespectful to take it back and this discussion is a bit embarrassing."
David DiStefano, the audit chairman, said the panel of five auditors named by local auditing associations "is not going to pay something commiserater with someone working in New York City. We're taxpayers too."
He said the requirement of a "super majority" for dismissing the auditor was put in "to insulate the city auditor against political influence that might occur from time to time."