A Liberal Democrat minister has said he might resign over the proposed increase in tuition fees.

Norman Baker, the junior transport minister, said today: "There are three options [voting for, abstaining, or voting against and resigning from government] and, to be honest with you, I genuinely haven't decided."

Earlier it was wrongly reported that Michael Crockart, a Lib Dem parliamentary private secretary, was going to stand down from his job in order to vote against the increase.

In a bizarre episode, someone claiming to be Crockart, the parliamentary private secretary to the Scottish secretary, Michael Moore, told the Evening Standard: "I will be voting against 100%. I'm not going to be pushed out. Resigning probably will be the only option."

Questions were only raised about his identity when the impersonator was interviewed on BBC Radio 4's the World at One, and colleagues realised it was not the Edinburgh West MP.

The Lib Dems released a more tempered statement on behalf of the real Crockart that said: "Discussions are still going on with parliamentary colleagues. I have not made a final decision."

The news about Baker comes as rebel Lib Dem backbenchers intensify their demands for this week's Commons vote to be abandoned in favour of a wider review of university funding.

His resignation threat follows an effort earlier today by former Lib Dem leader Paddy Ashdown to bolster support for Nick Clegg, who faces the strongest challenge to his authority since the formation of the coalition after he failed to broker an agreement on tuition fees with the party's president in advance of the Commons vote on Thursday.

Lord Ashdown conceded it might be years before Lib Dems saw any benefit from an "unpopular decision", saying that "at the moment they [the public] are just not listening". He added: "Nick could deliver the Sermon on the Mount; they are just not listening."

Ashdown said he would vote in favour of the tuition fee reforms when they reached the Lords.

When in coalition with another party there will always be "some things you like and some things you don't like", he told BBC Radio 4's Today programme. "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."

The coalition agreement reads: "If the response of the government to Lord Browne's report [into higher education funding] is one that Liberal Democrats cannot accept, then arrangements will be made to enable Liberal Democrat MPs to abstain in any vote."

Ashdown said the party was "going to go through its process" to hammer out a position, and each MP would have to decide whether they could support the measures. "I personally think that Nick has handled this with great wisdom and a great deal of courage," the former leader said.

Amid fears in Downing Street that Clegg is suffering a disproportionate amount of damage, David Cameron sanctioned a "rescue Nick" operation over the weekend to shore up his deputy's position, scheduling two announcements that would appeal to Lib Dem members.

David Gauke, the Treasury minister, today announced plans to deliver one of the Lib Dems' main manifesto pledges: to crack down on corporation tax avoidance. He will say legislation will be introduced next year to save £2bn – and protect a further £5bn – by tackling corporation tax avoidance, some VAT avoidance by companies and avoidance of income tax.

Separately, a £150m scholarship fund, which was unveiled by the business secretary, Vince Cable, will exempt up to 18,000 students from less well-off backgrounds from paying tuition fees in their first year at universities that charge up to £6,000. Students from poorer backgrounds at universities charging £9,000 a year would be eligible for an additional year of free tuition paid for by the university.

But the concessions have failed to sway senior Lib Dem backbenchers involved in intense negotiations with the leadership before the vote. This explains a weekend of mixed messages in which Cable announced on Friday that he would vote yes to the increase in fees, then said on Saturday he could abstain. Clegg clarified the leadership's intentions in the Independent on Sunday when he confirmed senior ministers would support the rise.

Clegg and other Lib Dem senior ministers such as Cable reached their decision after failing to broker a deal with Tim Farron, the party's newly elected president.

The group of Lib Dem senior ministers had told Farron they were prepared to abstain – dropping their preferred option of voting in favour – if he would follow their example. But Farron made clear that he could not break his pledge, signed by Clegg and most Lib Dem candidates in the general election, to oppose a rise in fees.

The failure of negotiations means that Lib Dem MPs could split four ways:

• Senior Lib Dem ministers will vote in favour of the increase on the grounds that Cable and Danny Alexander, the Lib Dem chief secretary to the Treasury, fashioned the policy. The ministers believe it is fairer than the current system because graduates would start paying back fees when they earned £21,000 rather than £15,000.

• A group of ministers and some backbenchers will exercise their right under the coalition agreement to abstain.

• A significant group of backbenchers will vote against the rise. This is expected to include Farron, Greg Mulholland, John Leech and the former leaders Sir Menzies Campbell and Charles Kennedy.

• Some MPs are prepared to vote in favour of abandoning the vote if there is enough support to table an amendment to the government motion on Thursday. A Commons early day motion, which accuses the government of failing to convince people that its proposals are fair and sustainable, could be turned into an amendment.

Clegg, who will address a meeting of his parliamentary party tomorrow night, believes his best aim is to ensure that the vote on Thursday does not lead to an outbreak of recriminations. One source said: "Nick would like everyone to vote yes. But that is not a realistic option. Everyone knew this would be difficult for the party. The aim now is to get through the week without any lingering bitterness."

But rebel backbenchers made clear they were spoiling for a fight. Mulholland, who tabled the early day motion calling for the vote to be abandoned in favour of a review of student financing, told the Guardian: "It is not in anyone's interests to do this at this stage. Sometimes the most courageous thing to do is to admit you need a rethink. The best thing for higher education is not to force this vote through on Thursday."

Today Mulholland told ITV's Daybreak: "This policy is not in the spirit of the coalition agreement. This is not a compromise; this is something that we could not possibly have envisaged being asked to vote on: a trebling of tuition fees; a lot of us simply cannot and will not accept [it].

"I'm saying to the government they really need to think again. They haven't convinced a considerable number of their own backbenchers, they haven't convinced the NUS, they haven't convinced future graduates and their families. They need to think again and ask those people how we can find a better way of doing this."