The Liberal Democrats ran into fresh trouble today when the party's higher education spokeswoman in the Lords, Lady Sharp, said she was not sure she could vote tomorrow for the coalition government's trebling of tuition fees.

Sharp told the Guardian: "I face a dilemma. I have a lot of reservations, and I am in the same position as many Liberal Democrat MPs. I have not decided how to vote."

Labour announced that it would stage a vote tomorrow to reject the Commons decision to treble tuition fees, ending doubts that Labour peers might feel constitutionally prevented from opposing secondary legislation.

Sharp said she was not sure the proposals would save the government money, adding: "That makes me question whether the whole exercise is worthwhile." She said: "The proposals will hit middle-income groups and burden young families with a household debt of £60,000 to £80,000 at an interest rate of 9%, just at a time when they are trying to raise a family and start a home. That is a serious disincentive."

She added that she could not agree with the government's calculations about the proportion of the student loans that will be repaid. She pointed out that, even on official calculations, £2.7bn of the £10bn due to be lent annually to students will not be repaid.

As the government is cutting £2.9bn from the universities budget, she questioned whether it would gain anything financially from the process, even if it takes the loans off the books.

Sharp's concerns have been backed by the Oxford-based Higher Education Policy Institute, the main independent thinktank devoted to higher education. Its director, Bahram Bekhradnia, said: "Our latest calculations on whether this package will save money show how much the government estimates are subject to very great uncertainty and are sensitive to very small changes. If the real-terms income of graduates rose annually by only 3.75%, rather than by the heroic 4.47% assumed by the government, then the package will not lead to net savings."

He said the government's latest concessions would increase the cost of the scheme significantly, lowering the likelihood of its leading to net savings in the long term. "We will not know for many years whether this scheme does save money, by which time it will be someone else's problem."

The thinktank's doubts about whether the scheme will save the Treasury money have been echoed by separate studies published by the Institute for Fiscal Studies and by London Economics. Ministers have repeatedly argued that the reforms are necessary to reduce the deficit.

Labour sources in the Lords said they could not predict whether they could defeat the Conservatives and Liberal Democrats tomorrow, pointing out that the two parties had a joint majority of 40, but the coalition had already been defeated six times since the election.

Labour's amendment will strike out the proposed increase in fees and instead urge the government to consult more widely and publish a white paper on higher education funding.

Lady Royall, leader of the opposition in the Lords, said: "Labour opposed the government's policy in the Commons last week, and Labour will oppose the government's policy in the Lords this week."

Though the Lords does not normally reject secondary legislation coming from the Commons, the all-party joint committee on the conventions between the two Houses of Parliament, which was chaired by the now Lord Cunningham of Felling, makes it clear that in certain circumstances it is possible for the Lords to do so. The Cunningham committee report was supported by all parties in both houses.

Royall said: "Cunningham makes it clear we have the constitutional right to do this, and the political imperative to do so is overwhelming."