As the D.C. Council prepares to finalize the city’s next budget, members appear to be deadlocked over whether to increase taxes on those earning $200,000 or more and how aggressively they want to push to hire additional police officers or fight proposed cuts in services.

Council Chairman Kwame R. Brown (D) began meeting with council members last week to gauge their priorities. Mayor Vincent C. Gray (D), who faced a $322 million shortfall upon being inaugurated in January, proposed his first city budget five weeks ago. That plan, for fiscal 2012, included higher income taxes for high earners and $187 million in spending cuts.

But Brown and several other council members are considering blocking the tax increase, which could lead to deeper cuts and set up a showdown with Gray and liberal council members who say the city’s wealthiest residents are not paying their fair share.

According to some council members, opponents of Gray’s proposal to raise the income tax rate from 8.5 to 8.9 percent for those earning $200,000 or more are one vote shy of the majority needed to remove the plan from the budget.

Brown, who as chairman has tremendous influence in shaping the final proposal members will vote on in late May, did not respond to a request for comment.

But several council members stressed that the proposed tax increase is one of several issues that could divide a body still reeling from recent ethics controversies involving Brown and Gray.

“It’s very fluid,” said council member Mary M. Cheh (D-Ward 3), who opposes raising the income tax. “What kind of cuts are we going to restore, and what kind of taxes are we going to reject? And if we restore cuts and reject taxes, where are we going to get the money to do that?”

Gray’s income tax proposal would generate about $40 million annually. Removing it from the budget, advocates and some council members say, could further strain social and human service programs.

Council member Jim Graham (D-Ward 1), chairman of the Committee on Human Resources, said he is struggling to find additional money in the budget for homeless services and mental health programs, both of which take big hits under Gray’s proposal.

If additional resources are not found, Graham said, all city-funded homeless shelters will have to close — including those designated for families — except on days of sub-freezing weather. “All those babies will be back to the stairwells, corners and cars,” he said. “There would be nothing beyond the freezing dates.”

Graham, a leading supporter of raising taxes on wealthier residents, said he also will urge his colleagues to come up with more money to improve security at Department of Youth Rehabilitation Services detention centers. Several juvenile offenders have escaped in recent weeks.

“We are at a fault line, I fear,” Graham said of the pending fight.

Council member Tommy Wells (D-Ward 6), chairman of the Committee on Public Works and Transportation, said the council also needs to come up with $13  million more to avoid reductions in city bus service.

Although he praised the mayor for presenting a “straightforward, honest budget,” Wells said the plan would create a shortfall in the Metro operating budget.

To avoid cuts in city bus routes, Wells said he may explore whether funding can be recouped from “additional fees, taxes or reprogramming” or revenue from other initiatives.

Council member Jack Evans (D-Ward 2), chairman of the Committee on Finance and Revenue, will probably resist any calls for higher taxes and fees. Instead, Evans is pushing to eliminate the proposed income tax increase and roll back parking meter increases implemented by former mayor Adrian M. Fenty (D).

“If the budget includes a tax increase, an increase in the income tax rate, I will vote no,” Evans said.

Evans’s position got a boost when Vincent B. Orange (D) was elected in the April 26 special vote for an at-large seat on the council. Orange, who is expected to be sworn in this week, campaigned as an opponent of raising taxes.

With Orange joining the council, there would be six votes against the tax increase. Brown, Evans, Cheh, David A. Catania (I-At large) and Muriel Bowser (D-Ward 4) have expressed opposition.

There are signs opponents may not have to look far for their seventh vote on the 13-member council. Yvette M. Alexander (D-Ward 7) joined a majority of her colleagues in successfully resisting a tax increase on wealthier residents in the current budget. Alexander said she supports Gray’s proposal but is willing to vote against it if Brown “is able to find money from somewhere else.”

But Alexander also plans to push for her own spending priorities. She said a greater share of the Health Department budget needs to be diverted to programs “pertaining to the health” of her constituents east of the Anacostia River, including diabetes, teen pregnancy, hypertension and heart disease.

“In the past, there has been a lot of focus on HIV/AIDS, which, of course, is a priority, too, but there are so many other issues, and that shouldn’t be the sole focus,” Alexander said.

Council members also are expected to struggle over how many police officers are needed to keep District streets safe.

The city has 3,880 officers, but under Gray’s budget the number could dip to 3,660, according to council members. Phil Mendelson (D-At large), chairman of the Committee on Public Safety and the Judiciary, said that he would like a force of at least 3,900 but that this will require $14 million more. Other members dispute Mendelson’s figure, saying it would cost far less.

“This budget is one of those times that separates the people with nerves,” Mendelson said. “There are a lot of programs, and we don’t have the money, so we’ve got to do the best we can and realize people are not going to be happy.”