The House of Lords is a "flawed institution" which exercises power without legitimacy, Deputy Prime Minister Nick Clegg has said.
Mr Clegg set out government plans for a smaller and mostly elected second chamber of Parliament on the first of two days of debate on the issue.
Many Tory and Labour backbenchers spoke out against the planned changes.
But the coalition says it is confident Lords reform, championed by the Liberal Democrats, will go ahead.
There has been criticism of the government's "programme motion" - due to be put to the vote on Tuesday - which would limit the amount of time MPs can spend discussing the issue to 10 days.
A letter opposing the current plans, signed by 70 Conservative MPs, has called for "full and unrestricted scrutiny" of the proposed legislation which will "pile a constitutional crisis on top of the economic crisis".
Signatories to the letter include a number of MPs elected in 2010, plus former Foreign Secretary Malcolm Rifkind and select committee chairs Bernard Jenkin, James Arbuthnot and Bill Cash.
During Monday's debate, Mr Rifkind told MPs that the government's proposals would create a "a sham democratic chamber which will consist overwhelmingly of members who would rather be in this chamber".
"I believe this bill has to be opposed because essentially what it is seeking to do will damage the fabric of our government," he said.
Labour says it will oppose the programme motion while Conservative MPs could be forced to resign from any front bench jobs if they rebel.
Conor Burns, aide to Northern Ireland Secretary Owen Paterson, told the BBC he expected to lose his job for opposing the bill.
Angie Bray, an aide to Cabinet Office minister Francis Maude, told MPs she had enjoyed working in his team but could not support what she described as "back of a fag packet legislation".
In another development, Lord Pannick, a senior lawyer and independent crossbencher, accused the government of failing to recognise the constitutional difficulties raised by its bill, saying it "does not adequately address" fears about the primacy of the Commons.
But amid raucous exchanges in the Commons, Mr Clegg urged MPs to support democratic reform of the House of Lords, which he said was needed to "get a grip" on the rising numbers of peers and make the chamber legitimate.
He said: "There are three reasons to vote in favour of the bill and its orderly passage. Because we believe in democracy; for the sake of better laws and because reform cannot be ducked.
"There will be those who are not interested in rational discussion. Those who will oppose Lords reform in whatever form, at whatever time, in whatever century, no matter what commitments their parties have made.
"This project has always been dogged by those who fear change."
Mr Clegg rejected the criticism of the amount of time set aside to debate the bill, saying there should be no more "foot dragging" on a project that had already lasted 100 years.
But BBC political editor Nick Robinson said Mr Clegg struggled to sell the proposals to Conservative backbenchers sitting behind him the chamber - who frequently intervened to raise objections.
Labour and the Liberal Democrats promised to reform the Lords in their 2010 general election manifestos, while the Conservatives pledged to "work to build a consensus" on reform.
The Conservative rebels say their party's manifesto pledge - and the coalition agreement's promise to "bring forward proposals" for an elected House of Lords - have already been fulfilled so they are not breaking any commitments by voting against the bill.
A cross-party group of parliamentarians in favour of an elected Lords has sent a pamphlet to every MP, calling on them to support the government's plans.
Labour's Peter Hain, who served in Gordon Brown's cabinet, said it was "now or maybe never for Lords reform" and it was time to "bring down the curtain on the longest political gridlock in the history of parliamentary democracy".
And former Conservative health secretary Stephen Dorrell said "the instinctive response which says that Conservatives are against House of Lords reform, and that current interest in the subject is the result of the coalition, is - in my view - wrong".
Speaking to the BBC, Labour leader Ed Miliband defended his party's position amid Lib Dem accusations of opportunism for planning to oppose the timetabling motion.
"I have said we want proper scrutiny of these proposals and will ensure they get into the House of Lords to be debated. I am not saying this bill will die in the House of Commons. I don't want that to happen."