It would limit elected officials to three terms, and it's been a big topic at city council meetings recently.
However, Monroe residents still have the chance to vote on it this November.
"Without my signature, it still ultimately becomes law as it relates to going out to voters in November," said Mayo.
The ordinance for term limits was approved for the November ballot by city council in February. If approved, elected officials would be limited to three terms. It would go into effect after this current term is over.
Mayor Mayo has threatened a veto saying voters already have the power to determine term limits every four years.
"Each and every time our citizens vote every four years, we consider that as term limits because they have an opportunity to vote for you as a mayor or council member," he said.
But the city charter prohibits his veto on the ordinance because it's a proposed amendment to the charter.
"By not having my signature, it says I don't support as mayor the ordinance for term limits," he said.
Mayo says unlike larger cities, mid-sized cities across the state and country do not have term limits.
"The size of our city, where people know each other, they communicate, they know if you're not doing a good job or not," he said. "They make that determination every four years and I think that's the way it should continue."
Monroe voters will have a say on term limits in November. Mayo said he's concerned about other ballot items at that time, like $1.6 million for milliages in safety service, recreation facilities and drainage facilities.
"Those are very important millages and I feel that those are being jeopardized for being on the ballot at the same time as this," he said.
Mayo also shared his concerns in the city council's actions recently attempting to find a council attorney, and trying to get rid of the city engineer position.
"I feel like the city council is quite frankly trying to gain more power," he said. "Charter clearly states that the city engineer has specific duties."
We reached out to several council members by phone for comment. District one councilman Ray Armstrong said he feels the mayor not signing the ordinance does not make a difference since it will go to voters in November.
Eddie Clark of District five said he feels the community will get to voice their opinion at the voting polls.
Gretchen Ezernack of district two said she voted against the ordinance because of the way it was written and defined, but said she is overall neither for or against it. She said the next step is to re-structure the wording in the ordinance for submission to be placed on the ballot. She said she hopes it will be more defined.
Kenneth Wilson of district four said he supports the ordinance because the community in his district has voiced to him that they support term limits.
"Three terms is twelve years, and we think that's long enough," he said.
Betty Blakes of district three could not be reached for comment.
Mayor Mayo said his goal is not to serve for a very long time.
"It's not self-serving being opposed because it is not my goal to serve an additional three terms," he said.
The mayor had 10 days from the approval by city council to make a decision on the ordinance. Mayo's decision on Monday not to sign marks the 9th day.