Almost 600 people have told council bosses how they think the Norwich Northern Distributor Road should join the A47 to the west of the city.
Four options for the so-called Western Link were unveiled by Norfolk County Council in November, with costs ranging from £60m to £161m.
The £205m NDR, now known as the Broadland Northway, currently ends at the A1067 Fakenham Road, but Norfolk County Council is committed to getting it linked.
At the planning stages of the NDR, now known as Broadland Northway, a link was considered, but ruled out because of the prohibitive cost of crossing the Wensum Valley.
But officers say talks with Natural England and the Environment Agency have given them hope a solution is possible.
A 30ft high viaduct could be built over the River Wensum and its flood plains, while one of the options would need a second viaduct over the River Tud.
Consultation started last November and ends in two weeks.
There are also a handful of drop-in events left where people can talk to officers.
Martin Wilby, chairman of Norfolk County Council's environment, development and transport committee, said: 'Given how important this link road is, we hope many more people will take the time to look through the information we've made available about our options and tell us what they think before the consultation closes.
'All the responses will be carefully considered and will help us to identify a preferred route for the Norwich Western Link as soon as we can.'
The idea of a Western Link has won backing from businesses, but critics, including the Wensum Valley Alliance and the Norfolk branch of the Campaign to Protect Rural England are worried about its impact on the environment and countryside.
The consultation, at www.norfolk.gov.uk/nwl, runs until Friday, January 18.
The final roadshows are: Aylsham Town Hall - Tuesday, January 8; Diamond Jubilee Lodge, Hellesdon - Thursday, January 10; Great Witchingham Village Hall - Friday, January 11; The Costessey Centre - Monday, January 14; Dereham Memorial Hall - Tuesday, January 15 and Honingham Village Hall - Wednesday, January 16.
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