Lib Dem councillor Jenny Dawe dismissed a claim Edinburgh was a "laughing stock", after figures revealed it would now cost £750 million to cancel the project or £770m to run the line from Edinburgh airport to St Andrew Square, against an original budget of £545m to take it all the way to Newhaven.
However, she was criticised by her SNP deputy on the local authority, Steve Cardownie, who said the tram scheme had been an "unmitigated disaster from the start".
Ms Dawe also found herself accused of "appalling complacency" by Lothians Labour MSP Sarah Boyack, after the council leader said there was a "way ahead" through the trams fiasco.
Speaking on BBC1's The Politics Show, Ms Dawe said: "We'll get through this, we'll get a tram and, in the run of things, I think that this will just be a small glitch on the way there.
"Clearly, nobody wants to see the city having reputational damage done to it, but I'm hopeful that we will get a way ahead."
She also claimed the "only option that makes sense" now was to take the line along Princes Street, rather than stopping at Haymarket to save money.
She made the claim ahead of a crunch vote by councillors on Thursday over a recommendation from council officials to complete the line from the airport to St Andrew Square, in the city centre.
Tory MSP Gavin Brown, the convener of Holyrood's economy committee, said Edinburgh taxpayers would take a "dim view" of Ms Dawe's comments.
"Anyone who describes this fiasco as a small glitch clearly is not living in the real world," he said. "I would hate to see what a large glitch would be if this is a small one.
"Enormous mistakes have been made with this project at just about every turn and the people of Edinburgh will take a very dim view of these comments."
Mr Cardownie said Edinburgh residents "might be a bit surprised" by the council leader's comments.
He went on: "It's not been a small glitch. It's been an unmitigated disaster from the start, and you can't downplay what's happened. I don't know the context of what Jenny said, but the Edinburgh public might be a bit surprised at this."
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