Council members Carlton Christensen and Stan Penfold did not support the tax hike.
The majority have asserted that at least $4.6 million of the increase is desperately needed for the Capital Improvements Budget to maintain the city's crumbling streets, rundown parks and aging vehicle fleet.
The council identified an additional $3 million for services to be added to the General Fund in the mayor's proposed $213 million budget for the year that begins July 1.
Last week, Love said she could only support a $7 million increase. She modified her position Tuesday.
"In looking over the numbers over the weekend, I'm willing to go to $8 million," she said. "No elected official wants to raise taxes. … But as a caretaker of the city, I believe we have to act today. Another year of neglect would only make things worse."
Historically, the council has held that 9 percent of the total budget should go toward maintaining the city's capital improvements.
But the Becker administration has not budgeted such funding during the recent economic downturn, said Simonsen.
For his part, the mayor has said he wants to have public discussions over the next year to ask residents about tax increases and service levels. In his annual budget address, Becker said that present service levels cannot be maintained without a tax increase.
Salt Lake City property owners this year will see a tax boost through Salt Lake County's parks and trails bond, as well as a Salt Lake City School District tax increase, the mayor said in a June 8 op-ed piece in The Tribune.
In addition, Becker said Salt Lake City taxpayers earlier approved a tax increase to bond for the new Salt Lake City Public Safety Building.
But Council Chairman LaMalfa said putting off maintenance outlined in the city's 10-year plan will make such fixes more expensive in the future.
"Our infrastructure is aging," he said. "In order to hold off future infrastructure problems we've got to get going."
Christensen said he voted against the tax hike because it would burden low-income residents and small businesses.
Penfold also voted against the increase, saying the public was not sufficiently involved in the decision.
The council held four public hearings on the budget, none of which was well-attended.
The mayor has 15 days to veto the tax hike.
If the council wishes to override the veto, it must do so by July 9.