The government has "no means" to help Liverpool City Council as it wrestles with a £17m shortfall in the funding for Capital of Culture year.
Mr Bradley said he was confident the events would be delivered
The warning came from Culture Secretary Tessa Jowell as she visited the city to hear a progress report from organisers.
Council leader Warren Bradley said he remained confident they would deliver a fabulous event.
The government also rejected calls for additional cash to help pay for extra policing during 2008 celebrations.
The budget for the 2008 programme is expected to be in place by October and, although there is currently a £17m deficit, Mr Bradley said the council was dealing with it.
"We are talking to the Treasury and we are talking to our own treasurers within the city council and I have got no doubt that we will deliver a fabulous Capital of Culture," said Mr Bradley.
"It's like any budget setting issue for the city council - we'll drive that - but not at the expense of frontline services or the programme for Capital of Culture."
Mr Bradley added that he had "no concerns" about the finances for the celebrations, which begin in 2008.
"As we said it is the programme that we presented within our bid and nothing has changed from that. It has not gone up and it has not gone down," he said.
The culture secretary was in Liverpool to speak to delegates at St George's Hall about Britain's "Cultural Olympiad".
'No bail out'
This will be a developing, four-year period of cultural activity designed to celebrate the Olympic spirit throughout the UK in the run up to London 2012.
Ms Jowell told the BBC that it was not the government's job to worry about the Capital of Culture shortfall.
"My department and the Arts Council has put in its share of the funding - £10m - so the council will have to find its committed £20m," she said.
"The council will have to sort this out. I can't come up and tell the council how they should spend their money."
Asked whether the government would step into bail them out, she replied: "We haven't got any means to bail them out."
In a separate development, a plea made by the Bishop of Liverpool, the Right Reverend James Jones, for extra funding for policing during 2008 was rejected.
He told the House of Lords that special funding for extra policing was approved for the month-long Commonwealth Games in Manchester.
Capital of Culture celebrations in Liverpool will last a year and are expected to bring an extra 24 million visitors to the city.
But Home Office Minister Baroness Scotland said it was up to Merseyside Police to make provisions from its budget.
"Monies that were made available in 2002 for the Commonwealth Games was because the Commonwealth Games was a specific, special event which was over a short period of time," she said.