Aldermen Bob Donovan and Mark A. Borkowksi sent a letter to Barrett on Wednesday outlining all the reasons he should resign.
"Too many agencies of this City's government have been roiled by scandal and mismanagement in recent months for this community to be able to afford a mayor with his mind and energy divided between the duties of his office and what promises to be a bruising political campaign," said the Aldermen in the letter.
They mentioned recent incidents such as the "shattered lead program," the firing of Milwaukee Fire and Police Commission Leader and the inability to improve regulations with the current administration in Madison as priorities for the mayor to devote his time to.
The Aldermen are concerned that Barrett will not have time to meet the commands of both positions if he enters the race for governor.
"During the best of times, this City needs and deserves a full-time mayor all of the time," said the Aldermen. "In these more difficult days, should you choose to run for governor, we ask respectfully that you step down."