Campaigners fighting against the felling of trees believe it is "unsustainable" for council contractors Amey to continue the work.
Works were due to resume this week after being put temporarily on hold last week and a council spokeswoman said a date for them to restart had still not been finalised.
Chris Rust, treasure of Sheffield Tree Action Groups, said "it looked as though Amey didn't have a plan at the minute".
"We have thought about it and if we put ourselves in their shoes, we don't know if there is an awful lot they can do to get back on the job
"We agree with Louise Haigh - the situation is unsustainable. Very large numbers of people are out on the street defying the security guards.
"We welcome the recent votes by several Sheffield Labour branches in support of our campaign and against outsourcing and the damaging PFI contract."
READ MORE: No date set for when tree felling works across Sheffield will continue
Mr Rust said the group had a "great deal of sympathy" for South Yorkshire Police and admitted it was "unreasonable to burden them with this mess".
An Amey spokeswoman said: "Amey is still reviewing their working practices and getting on with other elements of the contract - resurfacing and street lighting - at the minute.
"We will resume tree works as and when."