Fife asked for their forgiveness and understanding and support for his continuing to serve the city as mayor.
The week before Fife took his written confession to the Box Elder News Journal, council members met in closed session to discuss his indiscretion, and some urged him to quietly step down.
Utah law offers no recall mechanism to remove elected representatives from office. The council's resolution, if passed, can't force Fife to resign.
State Rep. Lee Perry, R-Perry, hopes to change that, however, and create a mechanism for voters to remove an elected official such as Fife.
At the urging of one of Fife's constituents, Perry said he intends to draft a recall bill that lawmakers can address during the legislative session that starts next month.
"We're going to file something that gives voters the right to decide if they feel a public official has done something inappropriate," Perry said. The official's behavior may fall short of being criminal, Perry said, and a recall law would give voters a way to get him or her out of office.
"Such a mechanism is important," Perry added. "I don't believe that voters should be stuck with their elected representatives until the next election."
Perry offered no opinion on Fife's situation specifically but said that if he personally were in similar circumstances, that "family comes first, and you need to do what's best for them. Public service is secondary."
Councilwoman Ruth Jensen said the resolution that will be voted on Dec. 20 is needed to show the public that some on the council don't support Fife's behavior.
"The council must do something publicly to show that we don't condone it," Jensen said.
Jensen acknowledged that she and other council members felt stymied by their inability to force Fife to step down.
"I would think his 40-year marriage would be most important," Jensen said. "It seems odd that he feels he has to stay involved in the minutia of the city. I'm dumbfounded that he thinks the city will automatically stop because he leaves."
Suresh Kulkarni, a retired engineer and longtime friend of Fife's, said he's personally urged Fife to leave office. Kulkarni lived in Brigham City until 2005 when he moved to nearby Perry.
"I told him as a friend that he should step down," Kulkarni said. "He's bringing a lot of ridicule on himself and his family."
Fife, who was excommunicated from the Mormon church and is taking steps to regain membership in the future, is praised by many as a well-educated, intelligent and capable man. Kulkarni agrees, but said the reason why he can no longer serve as mayor stems from breaching the public's trust.
"The city is essentially shut down right now," Kulkarni said. "Council members are in an uncomfortable situation, having told him to resign. My phone is ringing off the hook with people who don't want to work for this guy any more because they don't trust him."
Fife declined a phone interview Thursday. During a Dec. 6 City Council meeting, residents were divided as to whether he should stay or go. Fife has said that his conscience is clear and his commitment to serve is resolute.