Lord Ashdown has predicted the Lib Dems "will come through" their differences on tuition fees "holding together".
The former party leader told the BBC that would be a "significant achievement for Nick Clegg".
In Thursday's key vote Lib Dem MPs are to split three ways on plans to raise fees in England with some supporting, some opposing and some abstaining.
Meanwhile, David Davis has become the first prominent Tory to say he will vote against the rises.
The former shadow home secretary confirmed he would not support the plans in an e-mail to the National Union of Students' body at Hull University, seen by the BBC.
A spokeswoman said he had been a long-standing opponent of a rise and it had "always been David's stance whenever there has ever been any debate on tuition fees".
The Lib Dems vowed to vote against fee increases at the election, but have agreed to abstain in the coalition.
However, Mr Clegg and Business Secretary Vince Cable - whose department is responsible for the policy - have indicated they favour the policy and will vote in favour.
Lord Ashdown said he would have done the same were he still an MP - but fellow former leaders Charles Kennedy and Sir Menzies Campbell are set to vote against the fees rise.
Lib Dem transport minister Norman Baker has hinted he could resign from the government in order to vote against plans for tuition fee rises.
Earlier, Lord Ashdown told the BBC News channel: "At the end of this time we will make up our minds how we individually vote but if we agree to disagree the party remains united and that's a very significant thing.
"Have you seen a disagreement on this scale with the other parties in the past that has not ended up with rancour? I haven't."
He had told BBC Radio 4's Today that in coalition, there were "some things you like and some things you don't like".
He added: "Although there is a commitment that has been made during the election, there is another agreement we have to stick to which is the coalition agreement. That says at the very least you will abstain on this, vote for it if you can."
He accepted it would be several years before the Lib Dems saw any benefit from taking an "unpopular" decision, saying: "At the moment they (the public) are just not listening. Nick could deliver the Sermon on the Mount. They are just not listening."
Mr Clegg and his colleagues have faced criticism for backing coalition plans to raise university tuition fees to as much as £9,000 a year, despite pledging to fight any increase before the election.
According to the agreement with the Conservatives, Lib Dem MPs are expected to back the change in Thursday's House of Commons vote, or to abstain.
There has been mounting speculation about some Lib Dem MPs resigning from the coalition to vote against the policy, with transport minister Mr Baker calling it the "most difficult issue" he had faced.
Call for a delay
Asked on BBC One South East's Politics Show whether he would be backing the change or abstaining, Mr Baker said: "Or voting against. There are three options and, to be honest with you, I genuinely haven't decided."
He added: "It's an option if you resign. There are three options on the table and I haven't yet decided what I'm going to do."
Mr Baker, MP for Lewes, also said: "There's a meeting of the parliamentary party on Wednesday and I'll be listening very closely to my colleagues and we'll try to reach a common position if we can on that particular occasion.
"It's a very serious issue - and it's the most difficult issue I've faced frankly - but I want to get the decision right. I'm not going to tell you now because I haven't decided. I will decide before the vote."
The National Union of Students is promising to campaign directly against Lib Dem MPs who back the fees increase, arguing that the change will deter people from poorer backgrounds from going to university.
Lib Dem backbench MP Greg Mulholland is pushing for the vote to be called off, so that a full public consultation on the future of university funding in England can be carried out ahead of a government white paper in 2011.
He said: "There are very, very few who will support this motion. There are a few considering whether to abstain or vote against. But there are already a notable number who have decided that they will vote against this if it comes to it.
"And they are also saying, as I am, that really we shouldn't be going ahead with this because we've got ourselves into a mess and they only way out of this is to not have a vote on Thursday."
On Monday evening, a sit-in protest by about 100 students took place at London's Tate Britain ahead of the Turner prize announcement.
The BBC's David Sillito said police were also inside, but made no attempt to remove them.
Dean Kenning, one of the organisers, said: "It is a protest against fees but it is also about the competitive culture that the Turner represents."
Supporters handed out leaflets outside the building warning that higher fees could lead to empty art schools.