City department heads are requesting too much money from the city — $14 million too much.

Mayor Toni Harp told the News Tuesday that there is a $14-million gap between the aggregate funds requested by city departments and the revenue the city has at its disposal for the fiscal year beginning July 1, 2014. Based on preliminary departmental requests, spending would outpace revenue by millions of dollars, Harp said on Tuesday afternoon — less than three weeks before her budget is due to city alders on March 1.

Harp said she is elbow-deep with budget director Joe Clerkin trying to avert a hike in taxes. But the city will likely need roughly $14 million in additional funds to balance its budget should department heads get what they have asked for, she added. If she honors the agencies’ requests, a budget hole of up to $14 million looms.

“I don’t want to raise taxes,” Harp said. “We’re going to have to make cuts.”

The $14-million hole in preliminary calculations of the general fund does not even take into account the additional $5.3 million that the school district is requesting from the city, Harp added, saying the gap is really closer to $19 million.

At Monday’s school board meeting, New Haven Public Schools Superintendent Garth Harries ’95 revealed a total year-long spending scheme of roughly $396.5 million. A majority of funds will come from state Education Cost Sharing, but Harries said he would also be asking the city to up its contribution to help foot the school district’s operating budget.

“We want to do more for our students, not less, and that would require $5.3 million,” Harries said at Monday’s meeting. “That said, we know the city is in a difficult fiscal situation. We are talking with city officials to see what the potential is for this kind of budget increase.”

Harp stated bluntly that the city could not afford a $5.3 million increase in education costs. The necessary hike in property taxes would be untenable for city residents, she told School Board members Monday night.

The potential budget gap comes amid turbulent fiscal times for the city. All three major bond rating agencies downgraded New Haven at the end of last summer — with Fitch doing so twice, first from A+ to A and finally to A-. In January 2014, the Board of Alders replenished the city’s depleted “rainy day fund” — akin to New Haven’s savings account — by refinancing old city debt and shifting funds from bond payments down the road.

In her first month in office, Harp has taken a firm stance on fiscal accountability. At the end of January, she threatened to hold up Harries’ reappointment if he could not lower costs and present her with a balanced budget.

“We can’t afford to have another downgrade. It’s not acceptable,” Harp warned all department heads at the time. “They need to make corrections.”

Harp said Tuesday she could not yet speak to precise details regarding potential cuts — and what will be first on the chopping block. She said she would be meeting Tuesday with Clerkin to begin assessing those questions. Clerkin could not be reached for comment Tuesday.

The potential budget shortfall also heightens the need for state aid, Harp said. Though she said she is grateful for the small boost in Payment in Lieu of Taxes proposed by Connecticut Gov. Dannel Malloy, she will go “hat in hand” for additional contributions.

“If the [state] economy improves and the surplus deepens, that creates an opportunity to get more resources,” Harp said. Upgrades to information technology and more trucks for the Public Works Department are one-time payments that could be covered by isolated, single-year state contributions.

City Hall Spokesman Laurence Grotheer said each department head will be asked to defend the agency’s projected budget.

He said Harp still has time to bring requested spending into line with the reality of the city’s operating budget.

“It’s still preliminary,” Grotheer said. “There’s time to shrink that number.”

New Haven’s budget for fiscal year 2013-2014 is roughly $497 million.