The Government would have to rely on the Speaker's casting vote to get their university reforms onto the statute book if MPs could vote again on the Higher Education Act.
A poll of backbenchers by The Times Higher has revealed that enough Labour MPs would now change the way they voted in January 2004 to turn the Government's majority of five into a parliamentary dead heat.
Seven of the 19 Labour MPs who abstained in the vote to give the Higher Education Bill a second reading would vote against if they had the chance, while two MPs said they would now vote for the reforms.
One MP said that it was clear that the new system would not attract more working-class students into higher education - and that the most likely result was that poor students would "trade up" to elite universities and middle-class undergraduates would be crowded out.
Another said the size of the bursaries and student support being offered had persuaded them that the Government's reforms were right.
Two MPs said that they had decided not to vote against the Bill last year because of the timing of the second reading - the day before publication of the Hutton report on the death of the government scientist David Kelly.
"I wasn't prepared to risk bringing down the Government," one of them told The Times Higher .
But Ian Gibson, Labour MP for Norwich North and one of the key opponents of the Bill last year, said: "This shows that this is still a live debate and that everyone has moved on from their position a year ago. Now there are other issues looming large like course closures.
"But given the assurances we were given at the time, it looks like it will be difficult to persuade us to change things when the tuition-fee cap comes up for review in a few years' time."
Kat Fletcher, president of the National Union of Students, said: "It is not surprising that a number of backbenchers would vote against fees having seen how ill thought-out the whole legislation is."
Ms Fletcher added: "Considering that the majority of universities have chosen to charge the full £3,000 for courses, it is even more important that we keep the debate live and MPs continue to voice their grievances about the Bill over the next few years until the decision on raising the cap comes around."
A spokesman for the Department for Education and Skills said: "This is a completely academic exercise - the Higher Education Act received royal assent last year and there was a constructive dialogue in Parliament throughout the passage of the Bill."
Dead heats are settled by the casting vote of the Speaker of the House, who votes with the government of the day.