The local authority has prepared an emergency budget including 365 job losses and £22m in cuts to services because of the impact of the pandemic.
Describing the situation "as seriously grave", Labour High Town councillor Andy Malcolm told Monday's executive committee: "We've been forced to do this because of government intransigence.
"There's nothing forthcoming yet in terms of concrete funding for Luton to support us through the absolute disruption to our income through Covid-19.
"With nobody flying through the airport, coronavirus has meant a budget crisis for us.
"We are very much between a rock and a hard place, and there's no way out without government support, apart from this emergency budget."
A petition asking for extra funding has been signed by more than 10,000 local residents, which the council plans to present to the government this week.
Changes after the emergency budget will include a restructure of the senior management team, charges for brown bin collection, changes of the council tax reduction scheme and an end to the school meals services, the executive heard.
"It doesn't mean children won't receive school meals, because other providers will pick that up," explained councillor Malcolm, who added that councils have a legal duty to set a balanced budget.
"A lot of the loss of income relates to our airport company, London Luton Airport Limited," he said.
"The airport company is able to draw on reserves, but almost in their entirety to get through this year and this crisis.
"Our situation is more severe and more complicated than many other local authorities."
The council is spending reserves of £1.8m a month at the moment, while a further £3m savings are planned for the annual budget next February.
Labour Lewsey councillor Jacqui Burnett said: "I really grieve at having to do this.
"With the public health, we're having to step forward and provide a service, while the government has rolled us under a bus since the lockdown.
"I really hope we can come through, show how resilient we are and build our future."
Liberal Democrat group leader and Barnfield councillor David Franks said: "This emergency budget was put together in an enormous hurry.
"As a consequence, a number of the proposals are a bit vague and some are very complex.
"We will give a detailed response by the time it gets to full council."
The executive approved the emergency budget, which will be considered by the council on July 14.