, hosted on the TES website, asks teachers to detail the issues that they face in the classroom and suggest ways to tackle them. It has already been inundated with more than 30,000 responses.
The University and College Union (UCU) now wants the challenge extended to include specific issues faced by teachers in the further education sector, which has no nationally agreed employment conditions.
The union's general secretary, Sally Hunt, has written to deputy prime minister Nick Clegg, who helped to launch the initiative, and business secretary Vince Cable, whose department is responsible for the FE sector, asking them to help.
In the letter, Ms Hunt writes that the challenge is a "welcome initiative for a workforce under severe strain", but says she fears that the government has limited the consultation's reach and may miss the pressures on other educators.
"Many of the bureaucratic challenges faced by teachers in the school setting are also experienced by those working in colleges," she writes.
Ms Hunt goes on to say that FE institutions are subject to the same "stringent assessment" by Ofsted and cater for students from the age of 14, who are often vulnerable. "As a result, the scale of the paperwork is similar to that in schools."
Ms Hunt says that half of the UCU's FE members say they "always or often" feel pressured to work long hours, which has a "negative effect" on their professional and personal lives.
The UCU's most recent survey on stress and bullying found that more than a quarter of respondents worked in excess of 50 hours a week.
In all, 63 per cent who were employed on full-time contracts said they worked more than 40 hours per week, 24 per cent worked more than 50 hours and 5 per cent more than 60 hours.
However, Ms Hunt says that UCU members have many examples of good practice in managing workloads, which could be shared with the schools sector.
"Extending this workforce survey to those in further education colleges would allow this good practice to be shared, and common challenges to be identified and tackled in a more coherent way," she writes.
The call has been backed by the ATL teaching union, whose national official for pay and conditions, Steven Crane, told TES that workload was a "massive issue" for FE teachers.
He said: "Teachers and lecturers are equally under pressure in schools and colleges, so we have some sympathy with [extending the challenge]."
However, he said that the FE sector was in a different position from schools because of the lack of national employment rules. In FE, individual colleges set their own terms, leading to a wide variation in conditions; any issues are seen as a matter for the unions and employers to resolve between them.
Mr Crane said that the ATL was currently carrying out a survey of its post-16 members in England to get a better picture of their pay and working conditions.
According to the Department for Education, the Workforce Challenge survey attracted more than 6,000 responses within 12 hours of its launch.
All responses will be fed back to a panel of teachers and education experts in the New Year, which will work with the profession, teaching unions and Ofsted to put forward recommendations for change.
A spokeswoman for the Department for Business, Innovation and Skills (Bis) said that teachers working in FE were able to respond to the Workforce Challenge and that some had already done so.
"Bis will work closely with the DfE to identify responses from individuals working within further education to ensure that the information is reviewed by the relevant department," she added.
`It has got steadily worse'
Ray Amoss, a lecturer for electrical installation courses at Boston College in Lincoln, describes the workload in the further education sector as "horrendous".
"Most people work between 10 and 20 hours extra a week at home, marking and preparing for lessons, because otherwise the work just wouldn't get done," he says.
"It has got steadily worse over the past few years because of funding cuts, redundancies, pressure from Ofsted and the added bureaucracy.
"It is affecting teachers and support staff. There's a lot of stress. I know colleagues who have taken time off and even left the profession."
Mr Amoss says that the FE sector should get its own separate workload survey.