While Mayor Nutter was touring classrooms Tuesday and stumping for a soda tax to raise millions for city schools, Council members back at City Hall already were declaring his plan dead.

At least six of 17 members met in President Anna C. Verna's office Tuesday afternoon to discuss how to help the School District fill a $629 million budget gap - but without hiking taxes.

"I do not believe we can get the votes for a tax increase," said Councilman Wilson Goode Jr.

Nutter nonetheless plans to continue the fight, taking his plea for a soda tax directly to the public with a live address on 6ABC at 7 p.m. Wednesday.

Nutter spokesman Mark McDonald discounted assertions that the battle was over. Most Council members "realize that something very substantial needs to be done," he said.

"These kinds of very difficult issues are very fluid," he said. "They tend to solidify at deadline, at the time something absolutely needs to be done."

That time is fast approaching - there are just two Council meetings left until the summer recess, although one more can be added June 30. Council must pass the municipal budget by then or the city won't be able to spend money.

Nutter has proposed two options to aid the schools - a 10 percent property-tax hike and a two-cents-per-ounce tax on soda and sugary drinks. He has been pushing the soda tax as the more likely option.

Council plans to reconvene a committee meeting Thursday to consider voting out a tax proposal. The soda tax may have to emerge from that meeting to have any chance of passage.

Many Council members, however, are making alternative plans.

"Both taxes are pretty much DOA," said Councilman James F. Kenney, usually a Nutter ally. "We'll try to do as much as we can to get as much help as we can for the district."

If Council can't be moved on the soda tax, it would mark another significant defeat for the mayor. Council has turned back several of his major proposals, including previous plans to close libraries, enact a soda tax last year, and end the DROP pension program this year.

Nutter is sticking to this strategy: The state is more likely to help if the city comes up with some of the funding.

State Sen. Vincent J. Hughes (D., Philadelphia), the highest-ranking Democrat on the Appropriations Committee, said he had spoken with Senate and House Republican leaders during the weekend.

"Each one of them said that there is only one guarantee in this situation - that if the city doesn't add any new money to the table, don't expect Harrisburg to add any new money," Hughes said.

The city must act fast, he said. The state's budget deadline is June 30, but Hughes said his colleagues were likely to pass the budget early.

"I do know we're running out of time here in Harrisburg," he said. "The next couple days will be a very important time for the city.

Schools Superintendent Arlene C. Ackerman has asked for the city to pitch in an additional $102 million to help restore items in the district's $2.7 billion budget, such as smaller class size, accelerated schools, early-childhood services, counselors, and nurses.

Not getting the money would be devastating for schools, the mayor said. He attempted to illustrate the consequences Tuesday during visits to five schools, a tour he dubbed "Vote for Students."

"I think Thursday is a real judgment day, a real decision day for children," the mayor said. "It all comes down to do you support children, or not?"

Bridesburg Elementary School, where 70 percent of the students live below the poverty line, stands to lose all of its art and music funding and more than half of its funding for programs for gifted and talented students in the next school year. The school also will have to do without many of the support staff who Principal Jim Serpiello said had enabled the school to meet state standards every year.

"For a small school, that's devastating," he said.

Kathy Deputy is the mother of a student in the special-education program, which is slated for a 5 percent cut. She said she worried what the cuts would mean for her boy, who has thrived.

"Without funding, how can our school survive?" she asked.

Nutter also went to Baldi Middle School in the Northeast, Logan Elementary School in Logan, the Girard Academic Music Program in South Philadelphia, and Powel Elementary School in West Philadelphia. Those schools also stand to lose big - Logan, for instance, would lose all of its funding for reduced class sizes and a third of its money for school nurses. Powel would lose the allocation for its English as a second language program.

Council members who met in Verna's office said they were exploring whether they could give the schools some of the city's $51 million fund balance - its cash reserves - as well as possibly making other cuts to the city budget and directing the funds to the schools.

The Pennsylvania Intergovernmental Cooperation Authority, the state-appointed agency that oversees the city's five-year budget planning, has repeatedly warned against raiding the fund balance.

PICA Chairman Sam Katz said Council is left with few choices, all of them bad. He did not criticize Council for talking about tapping into the fund balance, but warned that it could come back to haunt the city.

"There could be a price to pay next year," he said. "It could come sooner than that."

City Finance Director Rob Dubow said taking $30 million from the fund balance - as proposed by Councilman Bill Green - would require $20 million in cuts, including eliminating a new class of police recruits and laying off 52 probation officers.

An additional $10 million would have to come from other areas, "potentially including laying off police officers, deactivating fire companies, reducing facility hours at recreation centers, reducing homeless shelter beds, reducing positions at libraries or other cuts in core services," according to a memo Dubow shared with Council.

The city would have to provide that money to the schools every year, Dubow noted.

A similar standoff happened during last year's budget talks, when the Nutter administration proposed a $64 million fund balance and Council reduced it to less than $43 million. Nutter and Dubow promised cuts and followed through - starting the "rolling brownouts," or temporary closures, of fire companies and the cancellation of two police academy classes.

A coalition fighting the soda-tax proposal staged a rally at City Hall Tuesday, with delivery trucks circling the building and blaring their horns.

Five Council members lent their support, including Councilwoman Jannie Blackwell, the education committee chair and a former teacher.

The coalition of the soda industry, store owners, and Teamsters has argued that the tax would be a "job killer," with shoppers buying their soda outside the city.

Harold Honickman, owner of the Canada Dry Delaware Valley Bottling Co. in Pennsauken, has been a leading opponent.

"The problem is it's a discriminatory tax against the poor and the middle class," Honickman said.

The coalition helped defeat the mayor's attempt to pass a soda tax last year, when it was proposed as an antiobesity measure. Honickman said he met with the mayor three weeks before the May 17 primary election and was told that there would be no new taxes.

Contact staff writer Troy Graham at 215-854-2730, tgraham@phillynews.com, or @troyjgraham on Twitter.

Inquirer staff writer Marcia Gelbart contributed to this article.