Many headteachers are against a government move which will require all teenagers to take GCSEs in traditional academic subjects, according to a poll.
It suggests that the vast majority of school leaders are concerned that the reforms will not suit every pupil and could mean less time for more creative subjects.
Under the change, children starting secondary school in England from next month will have to study English, maths, science, history or geography and a language at GCSE - the subjects included in the English Baccalaureate performance measure.
Ministers have said that this will ensure that pupils get a rigorous academic education, which will help them to succeed later in life.
But a survey by the Association of School and College Leaders (ASCL), found that many heads oppose the move.
Around 87% of the almost 1,000 members questioned last month said they disagree with the reform, while around 10% support it.
Of those opposed, 81% said that the range of subjects required is too inflexible, around 86% said it will leave less room for creative or vocational subjects, around 97% said it does not suit every pupil and 58% said the change is an unfair performance measure on schools.
Almost three quarters of those (74%) who said they had concerns agreed that more flexibility in the choice of subjects would make them more inclined to support it.
They survey also found that nearly three in four (74%) of school leaders said that their school does not have enough teachers for the EBacc subjects, with languages causing the most difficulties.
ASCL deputy general secretary Malcolm Trobe said: "We understand that ministers intend to consult widely during the autumn over their plan for compulsory EBacc, and we are very pleased that they are doing so. We hope that this will lead to them building more flexibility into this system.
"It is clear from our survey that the vast majority of school leaders are concerned that the current proposals are too rigid and will restrict their ability to offer a curriculum which suits the needs of all their pupils."
A DfE spokesman said: "We are determined to ensure that every child who is able studies the core academic subjects that will set them up for later life. For too long many pupils, and in particular pupils from disadvantaged backgrounds, were deterred from taking these subjects, which prevented them from reaching their full potential.
"The myth that the EBacc is having a negative impact on take-up of creative and vocational subjects was fundamentally disproven by last week's GCSE results, which showed an increase of 3.4% since 2010 in entries to art and design GCSEs.
"We are working with the sector to make sure there are enough teachers with the right skills and knowledge to allow pupils to study EBacc subjects at GCSE. Teaching remains a popular career and we provide bursaries for those training to teach many of the EBacc subjects."