The Sutton Trust education charity has published research showing four out of five young people in England and Wales expect to apply to university, but it warns that two-thirds would change their mind if fees doubled.
The poll also revealed that youngsters from poorer backgrounds were likely to be the worst affected.
The research comes against the background of Lord Browne's review of university funding in England which could allow universities to charge tuition fees higher than the current maximum of £3,225 per year.
Aaron Porter, NUS President, said: "These statistics are further proof that increasing the already crippling debt that faces students when they graduate from university would dramatically impact the number of young people able to enter higher education.
"If Lord Browne needed any further evidence that he should avoid both a market in fees, and an increase in student debt, this is compelling. It is vital that higher education remains open to all those with the ability, and we do not return to a time when it was just open to an elite minority."
Today staff and students at more than 70 colleges and universities will demonstrate against funding cuts in action organised by the United for Education coalition, which includes the Association of Teachers and Lecturers, the Educational Institute of Scotland, the GMB, the NUS, Unison, the University and College Union and Unite.
In a letter to the Guardian, they call on George Osborne to safeguard funding in tomorrow's budget, warning that further cuts in further, higher and adult education will leave thousands of teachers, lecturers and support staff facing the dole when they have never been needed more.