A Liberal Democrat peer and former party whip today urged Vince Cable to "bite the bullet" and ditch his offer to abstain on his own policy in a Commons vote in an attempt to prevent a party split over tuition fees.

Lord Willis, who retired as an MP in May, told BBC Radio 4's Today programme that the party had to get behind the proposals and start to "sell them".

Willis waded into the debate as many Lib Dems were wrestling with the fact that they made a pre-election promise not to support an increase but now find their leadership proposing a near-trebling of fees. The coalition agreement allows them to abstain on the issue, but many feel they must be true to their promise and vote against it.

Yesterday, Cable said he could be persuaded not to vote in favour of his own plan – his business department is in charge of universities – to increase tuition fees if it would help unite the Lib Dems, prompting an attack from Labour, who said it was "outrageous" for the minister in charge of a policy to contemplate not voting for it.

Cable's successor as deputy Lib Dem leader, Simon Hughes, has been pressing for the party to abstain. Nick Clegg, the deputy prime minister and party leader, refused to be drawn on the issue yesterday.

In a message to Clegg and Cable, Willis said that Lib Dems had to "get on board".

He told Today: "The reality is that we either bite the bullet and believe that the ... proposals ... are the ones to take us forward in terms of higher education or we don't. They do take us forward and it is time the Liberal Democrats now simply got on board and said, 'Well, let us back them; let us sell them.' I would like Nick to say that and I would also like Vince to say that.

"I hope Vince will reconsider that position [on abstaining]."

Some Lib Dems are determined to vote against the proposals – raising the cap on fees from £3,375 to £9,000 – in keeping with a pledge signed during the general election to oppose any increase.

Cable said yesterday: "If we all abstain, then that is the position I am happy to go along with. There is an option that we all abstain together and we are considering that."

Labour sought to keep up the pressure on the Lib Dems yesterday by using an opposition day debate to call on the government to publish more information on its proposals and to advertise Labour's view that the rise is being used to plug gaps left by cuts in government spending. Labour wants the white paper on higher education to be published before the house is asked to vote on it.

Yesterday the Welsh assembly announced Welsh students would not have to pay the increase in fees regardless of where in the UK they went to university.