Liverpool City Council's leader has said having to find savings of £91m has been "absolutely heartbreaking".
Labour leader Joe Anderson said he was "so angry and so devastated" at decisions the council has had to make.
Cuts revealed on Thursday will affect childrens' services, leisure centres, libraries, and voluntary groups, and result in hundreds of job losses.
Mr Anderson said everyone in the city would be affected by cuts which are having to be made.
"When somebody says every family or every service within the city is going to be affected, they are absolutely right," he said.
"And that's why your roads won't be getting cleansed as much as we want, there'll be no street cleaning as much as you used to get.
"Libraries will have to reduce their hours or close, leisure centres will have to reduce their hours or close, the potholes won't be getting filled.
"Every part of our life in this city is going to be affected."
The council has announced a package of cuts in its budget for the coming year.
It is set to cut half of its senior management posts, saving £4.5m, and has said the predicted figure of 1,500 job losses has been reduced to 1,200.
But funding for voluntary groups has been cut by £18m, a figure which represents almost 50%.
Mr Anderson said: "It's really hurtful to take £18m from the voluntary and community sector, because I know there will be hundreds of jobs going there and thousands of volunteers, and they offer support to the most vulnerable in the city.
"That hurts like hell, it hurts me and it hurts other people, I know that, but they're the types of decisions we are having to make."
Cuts in the government Sure Start grant will mean four children's centres will have to close.
Mr Anderson said those in Childwall, Hunts Cross, West Derby and Dovedale had been chosen as they serviced the communities with the least need.
He said: "We have managed to save 22 children's centres. Given the amount of funding we have had withdrawn, I think it's remarkable that we have managed to save them."
The budget has received cross-party support, a point reiterated by the leader of the Liberal Democrat group in Liverpool, Councillor Warren Bradley.
"I've always said you could put a cigarette paper between myself and Joe Anderson, in what we want for the people in Liverpool," he said.
"It's about making sure that we retain as many services for the most vulnerable people.
"So they can say, well actually they did hit us hard, but our cross-party politicians put forward a budget so that we could retain most of the services that we rely on in the city."
Mr Anderson has called on people to join a march through the city centre against the government cuts on Sunday.
It will be led by the Labour, Liberal Democrat, Green and Liberal councillors who worked together on the budget and attended by community and voluntary groups.