Civic leaders from across the north of England have gathered to discuss the dire state of rail services in the region.
The meetings in Leeds on Wednesday come as criticism mounts over the services provided by both Northern and TransPennine Express (TPE).
The firm announced it has cancelled dozens of services this month and Transport Secretary Grant Shapps said he wanted an urgent meeting with the operator to discuss its services, described by a boss of the firm as "not up to scratch".
Rail chiefs from TPE, Arriva and Northern attended the meeting and apologised for the recent performance, as RNA members described services as "shoddy" and a "shambles".
Criticism of Northern's services were compounded on Wednesday when the Yorkshire Post said a leaked report showed the firm has asked to be allowed to miss targets in its franchise agreement as it would be "significantly late" in refurbishing its fleet of trains.
Office of Rail and Road figures show just 56% of Northern trains arrived at stations within one minute of the timetable in the 12 months to December 7, compared with the average across Britain of 65%.
Appearing at the Rail North Committee (RNC) in Leeds on Wednesday, Mr Burnham said: "We are not prepared any longer to put up with, the people of our region are not prepared to put up with, the misery inflicted on their lives."
Speaking with reporters after a number of RNC members agreed with his proposal, Mr Burnham added: "The committee has addressed the idea of setting them a public deadline.
"We are now going to take a week or two to work out what form that takes."