Nick Clegg has urged his MPs to look at "all the facts" before deciding whether to oppose a rise in tuition fees.
The deputy prime minister said he would "understand" if fellow Lib Dems felt they could not back it, after signing a pre-election pledge not to do so.
But he said the Browne report, which recommended lifting caps on fees, could be a basis for a "fair and sustainable" model of future university funding.
Ex-Lib Dem leader Sir Menzies Campbell has said he will oppose any rise.
The government has broadly endorsed Lord Browne's report - which proposes an end to the annual £3,290 cap on tuition fees in England - but said it would look at the implications of lifting all restrictions before making a final decision.
Before May's general election, the Lib Dems agreed to phase out tuition fees over six years, while individual MPs signed pledges not to support any future increase.
Their coalition deal with the Tories allowed MPs to abstain from voting on the issue but Sir Menzies and former deputy leadership candidate Tim Farron are among those to indicate they will vote against any bill allowing universities to charge more.
'Lack of alternatives'
In a letter to all his MPs, Mr Clegg said he had personally "struggled endlessly" with the issue.
"I am painfully aware of the pledge we all made to voters on tuition fees ahead of the general election. Departing from that pledge will be one of the most difficult decisions of my political career."
But the assumptions underlying that pledge were no longer practical, he added, because the financial situation facing the country had changed completely and there were a lack of "plausible alternatives" to the framework set out in the Browne report.
Unless the current system was changed, he said either institutions risked going bankrupt or fewer students would be able to experience going to university.
Under Lord Browne's proposals, he said poorer students would pay less, wealthier students would pay more, the income level at which graduates would start to repay their loans would rise considerably and part-time students would get a fairer deal.
Going down this route rather than that of a graduate tax, which was "unfair and simply won't work", would leave the party on the "right side of the argument".
"I could not forgive myself if we did not take decisions now, regardless of how difficult they are politically, that would lead to a fair and sustainable system of higher education funding for future generations."
'Shot to pieces'
But Sir Menzies, Mr Clegg's predecessor as Lib Dem leader, said he was adamant that he could not support Lord Browne's proposal.
"I have the St Andrews University in my constituency. I am the chancellor of the university. My credibility would be shot to pieces if I did anything other than to stick to the promise I made," he told the BBC.
Lib Dem deputy leader Simon Hughes said the party's MPs must make their own choices on the issue and insisted there was time to improve Lord Browne's core proposals to make them "even more consistent" with what they had put forward at the election.
But students have warned that they will challenge MPs who "betray" pre-election pledges.
Lord Browne's review comes amid rising demand for places at universities which are unable to expand to provide them due to government spending cuts.
Further cuts are expected to be announced in the spending review on 20 October, as the government seeks to reduce the budget deficit.
Scottish students studying in Scotland do not have to pay any fees. In Northern Ireland and Wales, fees are charged up to a maximum of £3,290 a year.