Labour will "reach out" to Lib Dem MPs and supporters unhappy with the coalition and its policy on things like tuition fees, Shadow Business Secretary John Denham has told the BBC.
He said Labour must show it was not "tribal" with Ed Miliband as leader.
He said the party had worked very hard to try to head off the tuition fees rise and would continue to work with others who were "progressive".
But Lib Dem Simon Hughes urged "progressive people" to "stay with us".
Thge party's deputy leader was speaking on BBC Radio 4's The World This Weekend after holding talks with senior members of his Bermondsey party who are reportedly considering resigning.
Mr Hughes said the tuition fees issue could have been "presented better" and said that he wished he could have voted against tuition fees, rather than abstaining.
But he said he felt he had to abstain in the end because he could then register his opposition to the plans while not undermining the coalition.
He said it was now "critical" that the coalition showed it was the greenest ever government as well as taking action on civil liberty issues.
And his message to anyone thinking about leaving the Lib Dems was: "Stay with us - progressives are needed more now than ever in the party."
Earlier Mr Denham told the BBC's Andrew Marr Show he backed a graduate tax, although he acknowledged such a tax could end up being similar to tuition fees - but only if university funding was being cut by 80% as the government was doing.
He said Labour wanted a "fairer system" for graduates - adding the decision to stop funding most degrees was a political choice, not something forced on the coalition by the economic situation.
Mr Denham said it would be "middle income graduates in middle income jobs", rather than the wealthy who would pay the highest proportion of their incomes to pay off their debts under the government's plans.
He said that although the tuition fees rise went through Parliament "we worked incredibly hard, not just with Liberal Democrat dissidents, but people from other parties, to try to head this off" and he said this would be Ed Miliband's approach in the future.
Asked if he thought Labour could "break up the Liberal Democrats" he said: "I don't know. But what I do know is that there are many people in the Liberal Democrat and many of their voters who are deeply unhappy about the broken promises on tuition fees and the general direction of that party.
"I think it's crucial that the Labour Party is not seen as tribal and inward looking and sectarian but is willing to reach out to progressive people."
Chief Secretary to the Treasury Danny Alexander told the same programme that the coalition was "rock solid" and would last the full five years.
He also dismissed suggestions that Lib Dem leader Nick Clegg could face a leadership challenge, while deputy Lib Dem leader Simon Hughes said the party would recover as it brought in its "radical and distinctive" policies.
Former Conservative Prime Minister Sir John Major told Andrew Marr that Mr Denham's comments made his blood boil.
He said the Conservatives and Lib Dems had come together in the national interest and this was not the time for Labour to play party games.