Tony Blair's face-to-face meetings with Labour rebels over university fees have helped win support for the plans, the education secretary has said.
Blair spoke to MPs inside his room at Parliament
The prime minister spent about one-and-a-half hours seeing waverers after Downing Street branded Tuesday's vote as still "too close to call".
Education Secretary Charles Clarke later said he was "confident" the vote would be won.
"The prime minister always has an effect when he speaks to people," he said.
"He is one of the most articulate arguers there is.
"I have spoken to people, my colleagues have been speaking to people.
"And today people have been moving from that undecided category to say they will support us - whether enough we shall see, but I am confident."
Vote takes place at 1900GMT on Tuesday
The government has a majority of 161
If all opposition MPs vote against, it needs 81 Labour MPs to rebel for plans to fall
155 Labour MPs signed a motion opposing the Bill
Tony Blair says his authority is on the line with the vote
Hutton report due on Wednesday
The vote on the Higher Education Bill comes less than 24 hours before Lord Hutton's report into the death of weapons expert Dr David Kelly.
The two events combine to make this week Mr Blair's toughest since he was elected in 1997.
On Monday evening, Mr Clarke spelt out details of plans for an independent review to examine the impact of top-up fees three years after their introduction.
Over the weekend, he pledged to give legal force to his pledge to prevent fees rising above £3,000 per year until after at least two general elections.
Both measures are aimed at winning over wavering MPs, but potential rebels say they may not be enough.
Labour MP Jeremy Corbyn told the BBC: "What we are doing here is setting up two tiers of universities and introducing the concept
essentially of a graduate tax."
Austin Mitchell, one of the undecided MPs, told BBC Radio 4's PM programme: "To create a cliff-hanger like this with a majority of 161 demands absolute incompetence."
Asked if the government would win, the prime minister's spokesman said: "We hope so but we do not know."
He said Mr Blair was likely to continue talks with MPs on Tuesday.
In a sign of the vote's fine balance, nine MPs on a Commons committee have cut short a trip to Africa to return in time.
Meanwhile, Chancellor Gordon Brown has been campaigning for support for the plans.
He told an international enterprise conference in London: "I want us to be the best educated, best trained workforce and tomorrow's much-needed reform of university finance, which I urge all MPs, and Labour MPs to support, is another vital step towards that goal."