The coalition government is facing the prospect of its first major Commons defeat after a 70-strong group of Tory rebels signed a letter opposing House of Lords reform before a crucial vote on Tuesday.

The letter was released as Nick Clegg, the Liberal Democrat deputy prime minister, prepared to appeal for unity over proposals for an 80%-elected upper chamber as he opened a two-day debate on the bill on Monday afternoon.

Amid growing tension in the coalition and the threat of a mass Tory rebellion, Clegg has sought to cast the vote on Tuesday night as a test of David Cameron's leadership.

The letter, released on Monday, sets out objections to the contents of the proposed constitutional change, warning that Lords reform threatens to "pile a constitutional crisis on top of an economic crisis".

If all the signatories oppose the vote on the timetable for the bill, it will lead to the government's first significant defeat.

David Cameron's official spokesman reiterated the prime minister's position on reform of the Lords but declined to say whether Cameron had spent the weekend trying to persuade dissenting colleagues to back the government motion.

"No one should be in any doubt about his position on Lords reform. He is committed to these reforms," he said.

Asked whether parliamentary private secretaries who vote against the government's timetable can expect to be sacked from their unpaid roles, the spokesman said: "The usual rules apply, so members of the government are expected to vote with the government."

The spokesman defended the proposal for 10 days of line-by-line scrutiny in the committee stage of the bill's passage through the Commons as giving parliament "sufficient time to consider these proposals".

"They have been considered in detail previously. We have set out draft proposals and a joint committee has looked at them. There has been significant consultation. We have set aside a certain number of days for debate, but clearly parliament has other things to consider as well."

Cameron was not considering offering a referendum on Lords reform, the spokesman added.

Senior Tories, including John Whittingdale, chair of the influential culture, media and sport select committee, and loyalists such as Nicholas Soames are among those who have signed the letter, which concludes with an appeal to colleagues to ensure the bill is given the "full and unrestricted" scrutiny it deserves rather than the 10 days being offered by the government.

Outlining a raft of concerns, the letter concludes: "The commitments in our 2010 election manifesto and in the Programme for Government – to seek consensus and to bring forward proposals – have been fulfilled. We hope you will support us in giving this bill the full and unrestricted scrutiny it deserves."

The comment suggests Clegg has reason to fear the bill will run into trouble as rebels prepare to join Labour in voting against the "programme motion" – the timetable motion limiting the amount of time MPs can spend debating the bill as it goes through its remaining stages in the Commons. A separate vote, on the Lords reform bill's second reading, is expected to go through following the instruction of the Labour leader, Ed Miliband, to his party to support the bill at this stage.

The Lib Dems believe that without a programme motion the measure could be killed off because it would clog up the government's parliamentary schedule.

Mark Harper, the constitutional affairs minister, defended the proposed timetable in a last-ditch attempt to avert a large-scale Tory rebellion.

Harper pointed to comments made by Labour's Peter Hain in Monday's Guardian, in which Hain said that while he supported reform as a "now or maybe never" chance of change, he supported Miliband's decision to vote against the programme motion because he said he regarded it as a good opportunity to block the coalition's "rightwing" legislative agenda.

Harper told the BBC Radio 4 Today programme: "I've said to my opponents, they just need to look at what our opponents are saying in the Labour party. They want to vote for the principle of this bill, they want to vote against the programme motion to damage the rest of our legislative programme. That is what Peter Hain said this morning: he said he supports reform, but he doesn't want a programme motion because he wants to damage our programme. Let's debate this properly with a proper amount of time. But we don't need to debate it for ever."

But Conservatives usually loyal to the leadership joined the chorus of those opposed to the changes.

Soames not only signed the letter but also penned a column in the Daily Telegraph to describe himself as "appalled at the constitutional catastrophe" proposed.

The Conservative MP, who has only rebelled against the party leadership once in 29 years, wrote that it was with "the deepest reluctance" he had concluded he must do so again.

"The arguments offered in favour of the bill are entirely spurious," he wrote. "The House of Lords is not a failed institution: as the government's own white paper says, 'the House of Lords and its members have served this country with distinction'. The elected Lords will not be more accountable: on the contrary, peers will have non-renewable 15-year terms … No, this bill must be defeated at all costs."

Another signatory, Penny Mordaunt, told Today the bill was a "dog's breakfast".

Some Conservatives were angered by the intervention of a senior aide to Clegg, who said the Lib Dems would block parliamentary boundary changes in retaliation for a Tory rebellion.

The business secretary, Vince Cable, insisted his party was not issuing any threats or thinking of quitting the coalition and played down the prospects of defeat as government whips battled to control the revolt.