Concerns have been raised that millions could be added to the bill for the Norwich Western Link, due to delays and increased construction costs amid soaring inflation.
Mounting fears over whether the project can be delivered for the expected £198m price tag saw one councillor - who is backing the road - liken the scheme to "a boat with potentially a whacking great hole in it".
County Hall is also waiting to find out if the Department for Transport (DfT) will approve its outline business case and commit £168m towards it, with the council providing the rest.
Worried councillors called in the matter to the authority's scrutiny committee on Wednesday.
One of those calling it in was Liberal Democrat Dan Roper, a supporter of the road, which would stretch from the A1067 Fakenham Road, near the Norwich Northern Distributor Road, to the A47 near Honingham.
He said he was not prepared to "shut my eyes and hope for the best that things can work out", so sought information about what the increased costs might be and how risks over inflation were being managed.
Officers said they would not have a figure for any cost changes due to the route shift until June, after design work is completed.
They were similarly cautious about how much inflation and construction costs could add, but said they had factored in a £40m risk reserve.
Mr Roper, who represents Hevingham and Spixworth, queried if the council was asking the DfT for more than the £168m sought in the business case.
David Allfrey, the council's highway and major projects manager, did not directly confirm that, but said there was "an opportunity to talk to them about any changes" and that it was "unprecedented times", with regards inflation.
Mr Roper said: "There is a massive challenge now to the project. If this was a boat it would potentially have a whacking big hole in it. What are we going to do about plugging that hole?"
Andrew Jamieson, the council's cabinet member for finance, said he did not accept that premise.
He said there were a series of reviews the project would go through and such schemes were always funded through a mix of grants, council cash and borrowing.
Labour's Steve Morphew, chair of the scrutiny committee, estimated the cost of the scheme was now likely to be £250m, but Mr Jamieson said latest figures would be confirmed in June.
Officers did confirm £19m the government had already awarded the council towards the scheme would have to be repaid if it was not built.
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