The administration has said the tax rate would have to be set at about 1.25 percent of market value - $1,250 per $100,000 of assessed value - to collect the same amount of money as last year.
That rate would have to be higher if Council gives homeowners any kind of tax break when Nutter's property-tax reform, the Actual Value Initiative (AVI), goes into effect later this year.
Nutter is expected to propose tax-rate and relief measures in his budget address Thursday.
Kenney and other Council members have objected to the huge increases in tax bills that some residents of growing neighborhoods are facing under AVI.
His bill proposes a tax rate of 1 percent.
He said he had hired consultants to scour the budget for places to trim, and referred to "potential new avenues for revenue" without offering specifics.
Council members have proposed selling various city assets and allowing advertising on city property.
In other AVI-related news, Councilman Kenyatta Johnson called Thursday for the administration to extend by 45 days the deadline for property owners to file a first-level appeal of their assessments.
The deadline to ask the Office of Property Assessment for that review is March 31. The deadline to file a formal appeal with the Board of Revision of Taxes is Oct. 7.
Councilwoman Maria Quiñones Sánchez introduced a bill to create a central land bank that would bring all publicly owned vacant property under one agency, work to acquire other vacant and tax-delinquent parcels, and set policies for quickly moving land back to productive use.
The bill replaces one introduced last year and reflects feedback from Council, the administration, nonprofits, and developers.
Councilman Brian J. O'Neill introduced what he said would be the final amendments to his bill making changes to the new zoning code.
His original bill would have reverted to the standards of the old code for what kinds of businesses and other uses were permissible in commercial corridors.
That bill would have overturned four years of work creating the new rules, meant to reflect modern ideals of dense, walkable urban areas.
O'Neill said that his intent was not to return to the old rules but that the bill was a starting place to begin grappling with the implications of the new code.
"Many of the members understand it better," he said. "I know I understand it better."
O'Neill previously introduced an amendment that restored the right to start community gardens and urban farms in commercial corridors.
The final four amendments introduced Thursday address the density of apartments and require commercial activity in the first 30 feet of a building.
They also allow pet stores, groomers, and veterinarians in commercial corridors, but ban kennels, taxidermists, and crematoriums without a variance.
Finally, the amendments allow personal-care homes in commercial corridors only after community input.
O'Neill said that the administration was in agreement with the amendments and that he expected the bill to pass next week.
Contact Troy Graham at 215-854-2730 or firstname.lastname@example.org, or follow on Twitter @troyjgraham.