Wolverhampton City Council said in 2014 the authority faced the prospect of "becoming insolvent", unless it made "very deep and very fast cuts".
The Labour-run council approved plans on Wednesday to cut a number of services, including neighbourhood wardens, and increase council tax.
However, unions said they feared service standards would drop.
The council said the scale of cuts it would need to make by 2019 had risen to £134m - an increase on the £123m it predicted in 2014.
The authority said this was "largely due" to the rising costs of children's services, pay and pensions, and continuing government cuts.
In 2014, it announced it would have to cut 1,400 jobs and make massive service reductions or it would be down to its last £620,000 and "bankrupt shortly after".
Cabinet member for resources Andrew Johnson said: "We are now realistically looking at the prospect of becoming insolvent unless we make cuts."
The council said it had moved on "dramatically" since that announcement.
"This no longer reflects where we are," it said, in a statement. "The council has made it abundantly clear that it will do what was required to balance the books."
However, Wendy Thompson, leader of the Conservative group, said the authority had simply pushed its debt repayments back to give itself some "breathing space".
"That's they only way they are staving off this situation," she said.
"Their priorities over the years have been 'spend, spend, spend'. It's an unhappy situation for Wolverhampton. Our poor residents have a city centre that has so much dereliction and so many empty shops.
"We desperately need to turn the city around."
On Wednesday, the council agreed to axe the neighbourhood wardens service, despite a 4,500-signature petition from the public, and raise council tax by 1.99%.
Council leader Roger Lawrence said: "The savage cuts from central government that continue to unfairly target areas like Wolverhampton have made it impossible to continue to offer the level of services the city deserves."
Nick Keleher, secretary of the TUC in Wolverhampton, said the wardens did a "very useful job".
"The petition forced a debate in the council but now it is intending to cut the service despite the public campaign," he said.
"A lot of services have already been cut or transferred to the private sector.
"I have seen colleagues who have lost their jobs with the council move into the private sector. They have been very disappointed with the standards."
The government said: "Every bit of the public sector needs to do its bit to pay off deficit left by the last administration, including local government."
It said Wolverhampton's spending had increased during its time in office.
A council that said it feared becoming "bankrupt" has agreed to make a further £46m of cuts by 2019.