UPDATED: 2:30 p.m.
There will be "painful" changes in spending that will negatively affect city services and employees, he said.
"It's not going to be nice, and people will complain, and they're going to expect certain things to be done that aren't going to be done," he said. "But when there's no money, there's no money."
The only bright note he offered is that "it won’t be forever."
Kenney promised to deliver a significantly revised budget to City Council by May 1.
Kenney says the combination of a pandemic and recession is unprecedented in city history. Unlike the federal government, municipal governments cannot run a deficit, Kenney said.
"There's no playbook or script to this. It's going to be bad for a time, but we have to go through it. We have no choice," the mayor said.
So he promised a budgetary focus on the most-needed city services for the most-vulnerable citizens.
"We all must make sacrifices in the months ahead," he said, citing for example the sacrifices already made daily by the city's health care workers in the fight against COVID-19.
In honor of April 7 being World Health Day, Kenney said three-dozen Philadelphia buildings and landmarks will shine blue on Tuesday night.
For the city's Tuesday media briefing, the mayor spoke via video conference from his home, rather than his usual place at City Hall, in perhaps his strongest demonstration yet of the importance of social distancing.
He said going forward, the briefings would continue to be as virtual as possible.
Also speaking from home was Health Commissioner Dr. Thomas Farley, with another report on the continued growth of infections, hospitalizations and deaths across the city.
Farley reported 544 new COVID-19 cases since Monday, and a resulting total of 4,272. He said 20 more people had died since Monday, the city's highest number of COVID-19 deaths in a single day. The citywide count now stands at 65. And Farley said he expects the trend to continue.
He noted four new inmates in the city had tested positive since Monday, for a total of 58 COVID-19 cases in the prison system, adding that the city is working to make sure those inmates get the care they need.
There are 554 people hospitalized with the virus, Farley said, noting also that 40% of the city's hospital bed capacity is still available, and intensive care units in the region are not yet overwhelmed.
"We hope it stays this way," said.
If the city's medical facilities do get overwhelmed, Farley said, the city is welcoming retired doctors, nurses and physician assistants to volunteer for the city's Medical Reserve Corps.
"I’m hopeful that in the not too distant future, we will see a plateauing in the number of new cases of infections, but the number of people who die from this is going to lag behind, this so the number of deaths will probably rise in the next few days to couple of weeks," Farley said.
He said the testing site at Citizens Bank Park will be open through Friday and encouraged testing for anyone over 50, and any health care worker, who is showing COVID-19 symptoms.
Resources for testing and a host of other concerns are available online.
Pennsylvania looking for volunteers
In Pennsylvania, officials reported 1,579 additional cases, bringing the state total to 14,559. Officials said 76,719 patients have tested negative so far. The state also has a total of 240 coronavirus-related deaths in the state.
State Health Secretary Dr. Rachel Levine says the state needs volunteers now more than ever to help with the crisis.
“Volunteers are essential to distribute meals, donate blood, and help with so many other life sustaining activities for so many in our communities,” she said.
Tuesday’s increase in deaths, she explains, is directly related to how the information came in.
“There is sometimes a lag time for the reporting of cases and particularly deaths into our data system,” she said.