He noted, for example, that the city should be overlaying 245 miles of streets each year to keep up with its 10-year plan.
The proposed budget for fiscal year 2013-14, however, would allow only 5 miles of roadway overlay. And rather than completely rebuilding 18 miles of road, as it should according to the schedule, the city only can afford to rebuild 1.3 miles next year.
"I'm not seeing a sustainable future in our budget," LaMalfa said.
Councilman Charlie Luke said putting off maintenance of infrastructure further would, in the long term, cost taxpayers more.
"With the proposed budget, we're digging a hole that already is deep, even deeper," Luke said. "We need to do something this year to begin filling the hole."
Councilman Stan Penfold balked at a tax increase and said the council should use the next year to analyze and prioritize the city's needs.
As the capital city and host to visitors and commuters, "Salt Lake City residents bear a bigger tax burden than others for public safety and infrastructure," he said. "We can't put the entire burden on property owners."
Further, Penfold said the council should be more deliberate in its analysis before raising taxes.
"We're missing significant involvement from the community," he said of a proposed tax increase. "I have no ability to prioritize where we would spend it."
The council is seeking to get its capital improvements expenditures to 9 percent of the total proposed $213 million budget.
That would require about $6.5 million in new revenue, the equivalent of about $50 on a house valued at $250,000
In his annual budget address in April, the mayor conceded that revenues must be increased next year if the city is to maintain its current level of services.
On Friday, Becker's chief of staff, David Everitt, said the mayor is unlikely to support a property tax increase this year.
"The mayor thinks we need to take a year to educate our residents on what that [deferred maintenance] hole is and how to fill it," he said. "It's worth it to take the time so people understand the different options."
If the City Council were to pass a property tax increase this month, Becker could veto it. The council could override the veto, but it would require five votes.
Based on Friday's council discussion, those who appeared to favor a tax increase are Luke Garrott, LaMalfa, Luke and Soren Simonsen. Carlton Christensen and Penfold appeared less likely to support an increase.
The swing vote, if the mayor did veto a tax increase, appears to be Councilwoman Jill Remington Love. She said she could be convinced to support a "small to moderate" hike if the council analyzes priorities during the summer.
"The council is going to go through big changes next year," Love said of the November election. Christensen has said he will not seek re-election and Love may not either. "It would be irresponsible to leave this to a new council to deal with," she said.
The council will hold a 7 p.m. public hearing Tuesday on the budget at 451 S. State St., room 315. It must adopt the 2013-14 budget by June 22.
The Salt Lake City Council has scheduled a public hearing on the 2013-14 budget for 7 p.m. Tuesday in room 315 at City Hall, 451 S. State St.