The coalition will seek to head off one of the biggest rebellions on policy yet on Wednesday when MPs debate drastic cuts to the subsidies that have sparked a 39,000-job boom in solar power.

More than 20 Liberal Democrat MPs are likely to vote against the plans, in a revolt that observers say is likely to outdo the vote on tuition fees, when 21 of the party's number broke ranks.

The rebellion extends to ministerial level, with Norman Baker, the transport minister, writing to the climate secretary and fellow Lib Dem Chris Huhne to protest about the cuts, under which incentives to install solar panels would be halved, with potentially disastrous results for the fledgling industry. Baker said: "I have reservations about the speed and level of the proposed changes for community size projects [usually for panels to be installed on social housing] and I am therefore asking the secretary of state to examine urgently the case for some flexibility to mitigate any adverse effects of the changes."

Insiders say more than 40 Lib Dem MPs have expressed concern over the cuts, which are causing turmoil and job losses in solar companies – but, under pressure from the coalition whips, not all of these may decide to register their disapproval by voting with the opposition.

However, many are likely to be made just as uncomfortable by the extent of pressure being brought to bear outside parliament and among voters in key constituencies. On Tuesday, a rally against the cuts brought green protesters and solar industry workers to parliament.

Local government officials are also applying pressure– a briefing document seen by the Guardian shows deep opposition to the plans. In the document, the Lib Dems among the Local Government Association are vocal in their criticism of the cuts, acutely aware that environmental issues, and the creation of green jobs, are crucial issues for a large proportion of Lib Dem voters. The document says: "We fought the last general election on getting more green jobs. The feed-in tariff was helping to grow a new industry and get more people into work. We don't want to see this put at risk. [The cut] flies in the face of the government's hard work in schemes such as the regional growth fund and the Growing Places fund to help create employment."

Plans to halve the feed-in tariffs available for households installing solar panels were unveiled by ministers last month, after ministers took fright at media headlines attacking "green" subsidies and taxes as the source of energy bill rises – even though research by the regulator Ofgem and others shows fossil fuel price volatility to be the main cause of bill increases. They were also concerned that recent falls in the cost of solar technology meant companies were making excess profits from the panels, and that the boom in take-up would mean the £860m allocated for them would soon be used up.

Halving the feed-in tariffs for solar, however, is likely to save as little as 60p on an annual energy bill, which according to the industry would be outweighed by the loss of tax revenue and the impact of job cuts. They also point out that lower income households and those in fuel poverty are likely to be worst hit, as social housing landlords will find it hardest to get financing for installing panels, as will schemes for lower income households to have panels installed at no upfront cost.

Nigel Barnard, a director of Westward Housing Group, which is installing panels on 900 properties, said: "[The cuts] will have a considerable impact on our ability to help alleviate fuel poverty for many of our customers, though we are continuing to work hard to find positive solutions."

Most solar companies agree that, given the reductions in cost, the tariffs should be reduced. But they are concerned that the cuts are too deep, and the sudden introduction of the cuts – which will take effect from 12 December – is causing chaos as companies struggle to fulfil orders in time. Investors have also been scared off by the government's actions, as sudden changes to the subsidies make it hard to develop medium- and long-term business plans.

Several solar companies are bringing legal actions against the government, arguing that the rushed introduction of the cuts is illegal, because it is happening in advance of the consultation on the issue.

Labour, which introduced the feed-in tariffs late in its last term, is determined to take the government to task on the issue. Caroline Flint, shadow energy and climate change secretary, said: "The government's cuts to feed-in tariffs will hit families, put thousands of jobs at risk and destroy the solar industry. This is just the latest example of a government which is out of touch, cutting too far and too fast, with no plan for jobs and growth. They must think again, revise their scheme and extend their tariff deadline."

The debate is due to start at 4pm on Wednesday and finish at 7pm, but may run late due to other parliamentary business.