In 2019 the authority voted to replace the former Argos building in Newborough with a scheme drawn up in collaboration with Coventry University Scarborough and the York Teaching Hospital NHS Foundation Trust, which runs services at Scarborough Hospital.
As part of the plans, the council is also looking to create a "market square" which could include demolishing some buildings at St Helen's Square, which is adjacent to the Argos site.
The development still requires planning permission and now opposition Conservative councillors on the authority are calling for a fresh viability study into the project to be carried out.
The motion is being led by the deputy leader of the Conservatives, Cllr Heather Phillips, who told the Local Democracy Reporting Service that a lot had changed in the two years since the council signed off on the development.
She said: "We have gone through trade publications, we have gone through all sorts of stuff, and the percentage of increase in costs are quite staggering.
"In some instances products are going up 25%.
"They are having to pay higher wages and that is quite a major part of a building project.
"So, everything has changed since July 2019. Everything."
Cllr Phillip's motions calls for the "residents of the borough’s financial interest in the project to be protected" by a full review of the business case for the project to be carried out.
The project, which is being backed financially by Scarborough Council, will provide new retail units on the ground floor and accommodation for 52 in-training NHS doctors and nurses from Scarborough Hospital and 150 university students on the upper levels.
The existing building will be demolished to make way for the new development.
The leader of Scarborough Council, Cllr Steve Siddons, declined to comment on the motion ahead of the meeting when approached.