The city council has been left trying to find ways of filling a funding gap of £228 million after the decision was made to press ahead with construction of a line to St Andrew Square.
Council officials said that every £100m that has to be found is the equivalent of a 45 per cent increase in council tax.
City leader Jenny Dawe today insisted that the project would not become a "direct burden" on Edinburgh taxpayers and said crunch talks were planned with the Scottish Government on how the funding can be found.
Transport Minister Keith Brown has signalled that the Scottish Government was ready to help fund the trams by letting the city borrow against future business rate income.
Councillor Dawe's Liberal Democrat group has asked chief executive Sue Bruce for firm details regarding funding options and risks for building to St Andrew Square before any final deal with the contractor.
She insisted council tax rises were not an option.
She said: "There will be a huge amount of work done in the next few weeks as we try to look at funding options, but raising council tax is not one of the items that we will be looking at seriously.
"It is actually a national project so there should not be a direct burden on the Edinburgh council taxpayers."
Proposals include using "tax incremental financing" (TIF) - where the council can borrow against any future growth in business rates income that could be generated by building the tram - or persuading the Scottish Government to allow the council to keep a greater share of the business rates generated in Edinburgh.
Cllr Dawe insisted that, despite its opposition to providing more funding, there remained reasons for the Scottish Government to co-operate.
She said: "As far as the Scottish Government is concerned, the cancellation of Earl (Edinburgh Airport Rail Link] and the new station at Gogar makes the tram of key importance in meaning that people from other parts of Scotland find it easy to get to the airport.
"It has been made clear that they won't hand over a cheque with many zeros at the end but there may be other options they will consider."
Transport Scotland yesterday issued a statement saying that the decision councillors made on Thursday evening was "encouraging" but insisted that no further funding above the £500m already committed would be provided.
But Mr Brown gave a clear indication that the Scottish Government is ready to help look at other funding options.
He was asked whether either the TIF scheme, or bringing in a private contractor to build and run the operation, were possible ways forward.<!---
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