But with the Tories and Liberal Democrats promising to join Labour rebels to vote down the Bill, doubts are growing over whether the increases to tuition fees will ever be introduced.
Education Secretary Charles Clarke this week bowed to the inevitable and accepted that the Bill will be delayed to prevent a Commons vote on the issue before Christmas.
This prompted immediate concern from university vice-chancellors who warned that any delay in introducing variable fees of up to pound;3,000 per year could seriously damage the quality of higher education.
Mr Clarke also promised that the Government would consider raising the threshold at which graduates begin repaying their debts from the current pound;15,000 to pound;18-20,000.
But will this be enough to win over the rebels?
Much will depend on Gordon Brown, the Chancellor, whose allies are among the most prominent opponents of fees.
Mr Brown lost a Cabinet battle to introduce a graduate tax instead of top-up fees. He gave public backing to the plan this week but Blairites will expect him to put pressure on rebels to fall into line.
With Tony Blair in danger of suffering his first Commons defeat since becoming Prime Minister, the Chancellor is in a strong bargaining position.
While Whips twist arms, Blair and Clarke should reflect on just how they got themselves into this mess.
The student support reforms proposed will be a redistributive measure. They will remove a subsidy from the offspring of middle England and use it to provide more places at university for all. Yet a government famous for its powers of presentation finds itself opposed by left-wingers who normally criticise the Government for not being redistributive enough.
The British Social Attitudes survey, out next week, shows that there is little public appetite for greater subsidies to students. It places students a poor fourth in a list of popular education spending priorities, behind primary and secondary schools and pupils with special needs.
But the public remains unconvinced by MrBlair's scheme to ensure students contribute more.
Ministers' greatest problem is that they have been unable to combat media coverage playing on students' fears of debt while largely ignoring the fact that up-front fees will be abolished and graduates who end up with below-average incomes will pay back less.
During last year's long deliberations on higher education reform, Blairites rejected a graduate tax because focus groups found it unacceptable.
New Labour is beginning to learn that there are worse things than taxes.
Debt is one.