The Minister for Education and Science, Mr Dempsey, is facing increasing pressure to lift a cap on the number of places on Post Leaving Certificate (PLC) places next year.
This follows a unanimous decision by the Joint Oireachtas Committee on Education and Science to write to him expressing its concerns about the limit, which could affect some of the State's most disadvantaged students.
In a significant move, the cross-party committee has asked him to clarify his position on the matter and on the phased implementation of a report on the future of the sector.
Earlier, the committee heard a presentation from the Teachers' Union of Ireland (TUI), in which it said hundreds of students from disadvantaged backgrounds faced being left without places in September as a result of the limit.
Ms Annette Dolan, assistant general secretary of the TUI, told the committee there had previously been suggestions that the cap had been lifted, but this was not the case.
PLC courses, which provide vocational education opportunities to students from a wide variety of backgrounds, are currently offered to some 28,000 full-time students around the country.
However, while the staffing and funding for the PLC is normally based on enrolment numbers from previous years, in February 2004 the Department of Education instructed that PLC numbers be capped at September 2002 levels, which has lead to fears of significant cutbacks in existing courses and the loss of teachers.