The source said construction minister Brian Wilson had sent a letter to the FMB outlining his concerns and asking it to start to encourage members to join the scheme.
He said: "The government is losing patience with the FMB; now the scheme has been launched it is time for them to either put up or shut up."
He said the FMB could not continue to play a part in the scheme while it continued to "criticise and carp" from the sidelines.
The FMB asked for an appendix to be added to the official report into the review of the scheme that was sent to Wilson. This said the scheme would not work unless VAT was lowered on repair and maintenance and added that the cost of joining the scheme was too high.
Brian Flint, deputy director general of the FMB, said he had sent a letter to the government asking for more time to resolve the issues.
He said any official inquiry would be dealt with responsibly.
A DTI spokesperson said the FMB's concerns about the quality mark would be eased if members tested it out in a pilot.
She said: "The quality mark had been trialled successfully by other trade bodies for some time and we would be very pleased to see the FMB support the scheme in this way."