More than 60 people trooped to the microphone Monday to plead with Richmond City Council not to cut programs they need.

One of the biggest contingents included people who found jobs because of help from the city’s Center for Workforce Innovation. They urged the council to restore $400,000 to the city budget to enable the program to hire six additional people to help the unemployed secure work.

Members of City Council were sympathetic, but essentially shrugged their shoulders.

So far, the council has spent at least 16 hours going through Mayor Levar M. Stoney’s proposed spending plan for fiscal 2017-18 that will begin July 1. They are trying to find cuts in order to fund their top priority: Improving the pay of veteran police officers and firefighters to keep them in the city. The total cost: $2.7 million.

As the council completed its latest five-hour budget session on Wednesday, it was still $100,000 short of meeting its goal on police and firefighter pay.

As they left, most members were mulling whether to take $6.8 million of the $8.3 million in savings the Richmond Public Schools has built up during the past four years to ease the pressure. They have asked Mayor Stoney to certify the money is available.

The decision on whether to use that money for city needs is likely to come when the council meets again Monday, May 1, to try to complete their amendments to the Stoney spending plan.

Surprisingly, City Council appears to be ignoring another big fund it could tap — the city’s own savings account that has grown fat even as funds for operations seem to get tighter.

On Monday, even as they listened to residents seek money for programs, they also learned that the city had generated a $13 million surplus from the 2015-16 fiscal year that ended last June.

The disclosure came as the administration released the final draft of the long awaited audit for that year — five months late.

The $13 million surplus is far larger than anticipated. It is nearly three times larger than the $4.5 million surplus that the administration originally projected in September, and a big turnaround from 2015 forecasts that the city would finish the 2016 fiscal year with a $12 million deficit.

So far, every cent of that money has been put into the city’s “rainy day” fund, or unassigned balance.

The result: The city’s “rainy day” fund as of June 30 ballooned to $98 million — equal to about $430 for each of the city’s 221,000 residents. The total is a 15 percent increase from the $84 million the fund held on June 30, 2015.

City policy requires the fund to hold a minimum of 10 percent of general fund expenditures. Based on the $681 million spending plan the mayor presented, that would mean $68 million.

Mayor Stoney and his administration are proud of the surplus and are seeking to beat back any perceptions that city operations are being starved to maintain far more savings than required.

According to the city’s financial adviser, Roland Kooch of Davenport & Co., the savings account is good news for the city.

He said the “healthy” fund balance enables the city to avoid taking out short-term loans in the fall to fund operations before annual tax receipts begin arriving in the spring.

He said having a large rainy day fund also has helped the city raise its credit rating and borrow at lower rates, saving taxpayers money by reducing the interest on loans.

The savings also means funds are available if the city had to deal with a natural or man-made catastrophe, he said.

But it is unclear if the council would damage the city’s credit if council withdrew $3 million to $4 million to cover one-time expenses and free up money to pay for higher wages.

City Council President Chris A. Hilbert said the council has pulled back from the idea. City Attorney Allen L. Jackson on Monday cautioned about tapping the fund as they would not know if the fund was expanding or contracting until the next audit for fiscal year 2016-17 was issued, possibly by the end of November.

However, in response to a Free Press query, Mr. Jackson acknowledged that the council, during the budget process, has full control of the money.

He said the only potential barrier is a 2012 policy resolution that limits the governing body’s ability to tap the rainy day fund, but he also said that the council could vote to ignore the policy.

So far, council members have shown little appetite to take money from that pool.

On Wednesday, council also turned thumbs down on the idea of creating new taxes or raising existing taxes, including a tax on cigarettes or the restaurant meals tax.

The only revenue-raising proposal that has gained support is a proposal to seek to charge a service fee to three state authorities with large property holdings in the city. The authorities do not pay property taxes.

Fifth District Councilman Parker A. Agelasto has been pushing to gain payments in lieu of taxes, or PILOT, from the Virginia Housing Development Authority, the Virginia Public Building Authority and the Virginia Biotechnology Research Park Authority.

He indicated that if those authorities could be induced to pay the PILOT, the city could generate about $1.1 million in new revenue. His plan is now included in the council’s proposed amendments.

The council is racing to complete its work and pass its version of the budget by Monday, May 15.