The call was made at a scrutiny meeting of the council to discuss the problems surrounding the new vessel.
Council leader Dave Stewart said the crossing at Cowes would be free until 2 July "in recognition of the problems" and to allow feedback.
Mr Stewart said the council had ordered a review of the project by auditors.
He said it had been a "frustrating and disappointing start" to the ferry.
Since launching late on 14 May the chain ferry has broken down, run aground and been suspended by the Maritime and Coastguard Agency due to "training issues".
Cars have also been damaged getting on and off.
Shopkeeper Angie Booth, who owns Valu-4-U in East Cowes, said: "Whether I come out of this and survive I am not sure - other businesses too. We are bearing the brunt of the loss of almost six months of trade.
"Will you compensate local businesses, the same as for damaged cars?"
Transport councillor Ian Ward said compensation was up for discussion.
He added: "I don't think it's a disaster. It's a prototype. There are bound to be teething problems. There were electrical problems which the company has rectified."
He said the council authorised the manufacture of ramp extensions to resolve the problem of vehicles scraping the concrete.
He said groundings were an issue with seamanship, which had been resolved.

Alasdair Dudgeon was killed near the Kincardine Bridge on 6 January 2013 when James Sneddon knocked him off his bike in the early hours of the morning.
Mr Dudgeon suffered a broken neck and internal injuries as he commuted to his work at a bakery near Falkirk at 02:00.
Sneddon, 42, was found guilty of causing the 51-year-old's death, after a trial at the High Court in Edinburgh.
Mr Dudgeon, of High Valleyfield in Fife, regularly cycled to and from his work as a baker at Tesco in Camelon, just outside Falkirk.
He was cycling on the A985 road between the Longannet roundabout and the Kincardine Bridge when he was hit by a Vauxhall Astra driven by Sneddon, of Falkirk.
Sneddon called an ambulance, but paramedics found no sign of a pulse on the victim before taking him to Forth Valley Hospital in Larbert, where he was pronounced dead.
Witnesses said weather conditions were clear and visibility was reasonable on the night of the crash, with a police officer noting that the red flashing light on Mr Dudgeon's bike was bright enough to be seen from 300m away.
Prosecutors said that although Mr Dudgeon had not been wearing a high visibility jacket, Sneddon should have seen him well before the collision and should have taken steps to avoid the cyclist.
The Crown originally charged Sneddon with causing Mr Dudgeon's death by dangerously failing to observe the cyclist and colliding with the rear of his bike, which he denied.
After a trial, the jury found him guilty on the lesser charge of death by careless driving. He will be sentenced later after background reports are compiled.
Shopkeepers near the Isle of Wight's troubled new "floating bridge" have asked councillors to consider compensating them for loss of business.
[NEXT_CONCEPT]
A motorist who fatally injured a cyclist has been convicted of causing death by careless driving.