Farmers' Union of Wales president, Bob Parry, is set to demand Christine Gwyther's resignation to her face in a meeting on Monday.
Mr Parry is leading beef farmers who insists Ms Gwyther will not be able to promote Welsh meat credibly.
Pressure has grown steadily in the 10 days since the 'veggie minister' was first appointed.
Farmers staged a picket on Sunday outside a hotel in mid Wales, where Ms Gwyther and the Welsh cabinet were holding a weekend "getting-to-know-you" session.
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Farmers believe the agriculture secretary is in an untenable position to promote sales of Welsh livestock, which make up 80% of agricultural income in Wales.
Mr Parry hinted that if Ms Gwyther refused to go, farmers would stage a protest at the state opening of the new National Assembly building in Cardiff Bay on Wednesday, which will be attended by the Queen and Prince Charles.
Already angered by the beef-on-the-bone issue, GM "double standards" by the government and dwindling incomes, the FUW is likely to press home its stand on the issue of Ms Gwyther.
"Time is running out. If she is there for six months and it does not work, then many farmers will have gone out of business, just by giving her a chance," said Mr Parry.
"I believe we need a person in position that will go out into Europe and sell our products, especially the red meat sector."
Ms Gwyther had only been in the post for two days when it was revealed she has been a vegetarian for 20 years, prompting surprise then anger amongst Wales' livestock farmers.
Happy for people to eat Welsh meat
But the agriculture secretary has stood firm in her belief she can do the job, pointing to her previous work at Pembrokeshire County Council, dealing with farmers and butchers.
"It is not my job to tell farmers what to think, really," she told BBC Wales.
"My whole brief from the start has been because I am very concerned with animal welfare, I am happy with people eating Welsh meat rather than meat from other countries, which does not have the same standards.
"I see that sitting very easily and very comfortably within my own philosophy and beliefs."
Ms Gwyther said Alun Michael had known she was a vegetarian before her appointment.
Assembly may vote on beef ban
(20 May 99 | UK Politics)
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