Sheffield Council leader Julie Dore is pushing for greater devolved powers as the consultation on devolution begins.
Chancellor George Osborne visited the region in October to sign a proposed deal that would offer £900 million over 30 years in exchange for an elected mayor in 2017.
Only half of the combined city region would be able to vote for the new mayor under the current deal. The proposal would also give the mayor powers to veto every decision.
Labour councillors say they are instead pushing for the model in Manchester, where two-thirds of the local council leaders can ovverride the mayor.
Coun Julie Dore said: “It is important that we do not just agree to a deal which as it stands could be damaging for the future of the region just to benefit the short term political interests of George Osborne.
“We desperately need investment to deliver real change. We will not allow devolution to become a way for the government to pass responsibility for cuts downwards. George Osborne has talked big about the Northern Powerhouse, but that’s all it has been so far: empty words. As it stands, Sheffield is not in a position to support these proposals without the changes we have set out.”