The developer, often heralded as the socially aware white knight of urban regeneration, is coming in for flak from the city's Liberal Democrats, who have launched a campaign to flatten the 1960s concrete behemoth.
The powerful opposition party, which is hoping to overturn a small Labour majority at the forthcoming local elections, feels Urban Splash is stalling over the deal to take the Grade II*-listed buildings off the council's hands.
Local Lib Dem councillor Arthur Dunworth believes the current negotiations favour the developer, and that the £35 million needed from the council to support the £163 million revamp could be better spent on a range of other projects.
He said: 'It seems to me the numbers have started changing and the whole thing on which the scheme was sold is changing too.
'There will be no guarantee the private money will be forthcoming. It does seem to me that the chance of getting this off the ground is less down to our side and more to do with the private sector.
'The scheme is not within the gift of the local council and we don't want this to be open-ended. That's the Wembley scenario.'
Dunworth also feels the VAT position on refurbishment - which is the normal 17.5 per cent, as opposed to new build which is zero rated - has also become a stumbling block.
He added: 'It's gone quiet, partly because of the whole premise of VAT relief. The VAT relief element has become more problematic than we first thought.'
However, Urban Splash's director of development Nick Johnson has rubbished claims that the scheme, which is being designed by Studio Egret West and Hawkins\Brown, is not on schedule.
He said: 'All the comments raised have to be taken in the context of how delicately poised the political situation is and in light of the forthcoming local elections.
'We are cementing all the funding packages and we are confident we have got the right solution and the right public-sector support.'
In respect of the VAT situation, Johnson maintains that there are a number of options open to them, several of which are being considered by HM Revenue and Customs, such as whether there will be sufficient amount of new build to be given VAT exemption. There are also other avenues available because of Park Hill's listed status.
Nevertheless, Johnson admits that he has not had to work in such a political cauldron before.
He added: 'This scheme is under the political spotlight. It is not a situation we have particularly come across in the past. We have done all the tough groundwork away from this spotlight.'
Meanwhile, a Sheffield City Council spokeswoman confirmed that the project was still on target and that key negotiations were currently ongoing. She added that the council 'was not concerned that anything was likely to change'.