Bailiffs have visited the council, some suppliers have withdrawn goods and services, and staff say workers have been forced to use their own money to buy food for a children's care home.
The council's IT transformation programme, which included the SAP project, was among the winners of the Cabinet Office's E-Government Awards. Gordon Brown praised the awards winners last month.
Glyn Evans, lead for the council's IT transformation programme, said, "Some individual suppliers have gone through some pain. I regret that."
The council ran into difficulties after the project went live last October. Problems included the partial failure of the automatic installation of SAP software on about 5,000 PCs. This meant software specialists had to visit each machine and load the software manually.
The delays left staff who were without SAP unable to pay invoices. When some business users called the helpdesk, they were unable to obtain assistance for 48 hours.
The council's joint IT venture with Capita, Service Birmingham, which supplied the SAP system, has brought in extra staff to clear the backlog of invoices. The council concedes that the cost of sorting out the problems will reduce the profits of Service Birmingham.
Council officers expected teething problems when the SAP financial system went live on 29 October last year. But Evans said the council had expected the backlog to have been cleared by December 2007. Now they expect to clear it by the end of this month.
The backlog needs to be put into the context of the scale of Birmingham City Council's operations, he said. It has a turnover of £3bn, pays £1bn a year for goods and services and settles 700,000 invoices annually. Evans said he was aware of bailiffs being called to only one site.
He said the SAP-based Voyager system has paid 216,000 invoices successfully to about 20,000 suppliers. Voyager is one of nine major transformation programmes within the council. The council hopes the whole programme will save £1bn over 10 years.
Birmingham MP John Hemming defended the system by writing to a local blogger, The Stirrer, after council staff used a forum on the website to complain about Voyager.
He said, "There is a backlog which is being cleared." He added that bailiffs only visited one council site after a supplier's bill was only "three days late".