Construction of the new Forth road bridge will get under way next year, under plans approved by MSPs.
The Scottish Parliament passed, by majority, new legislation needed to build the £2bn crossing, due for completion by 2016.
Ministers say the condition of the existing bridge, linking Edinburgh and Fife, is deteriorating.
The project has come under attack from environmental campaigners and there has been a row over how to fund it.
The Scottish Greens are now leading calls for public spending watchdog Audit Scotland to look into alternatives to the crossing before contracts are arranged.
Backers include WWF Scotland and Friends of the Earth Scotland.
The bridge, to be paid for by the Scottish government's capital budget, was brought forward in the wake of concerns about the condition of the existing crossing, now more than 40 years old.
The replacement link, to be given the green light under the Forth Crossing Bill, has been described by the Holyrood government as the biggest Scottish infrastructure project for a generation, and vital to the economy.
The existing road bridge would be used for public transport and cyclists.
Scottish ministers clashed with the previous Westminster government over borrowing from future budgets to pay for the crossing.
The SNP said the project would be delivered on time and on budget.
The campaign group Forthright Alliance has argued the new bridge - to cost between £1.7bn and £2.3bn - is not a "justifiable or credible" use of public money.
Lawrence Marshall, from Forthright Alliance, said work to slow down the cable corrosion would be enough to save the current bridge.
"The cable drying has been working," he said. "There is a slow and steady decline in the humidity within the cable and if you can manage to dehumidify the cable then basically the corrosion will have much less chance of increasing.
"If you halt the corrosion getting just a little bit worse than perhaps it is at the moment then you still have a buffer in order to be able to operate the bridge."
However, Tricia Marwick, MSP for Central Fife, said delaying work on the new bridge was not an option.
She said: "Even if you are able to halt the corrosion, then we have lost a lot of the strength in the bridge already.
"It is absolutely imperative that we press ahead with this work. We can't wait to see whether the work on the cables may halt the corrosion.
"We have got to ensure that there is a passage from the Lothians to Fife after 2017."