Lib Dem leader Nick Clegg is the driving force behind the bill, which would replace the current mix of 826 hereditary and life peers with a chamber of around 450 members, most of whom would be elected.
But Conservative rebels said the reforms would threaten the superiority of the lower chamber.
Ministerial aide Conor Burns said he is willing to resign his post in order to vote against the government on the issue.
“If I lose my job for something that was a mainstream view within the conservative party within the last parliament, which serving cabinet ministers held as their view, so be it,” he said.
Tory MP Eleanor Laing echoed his view: “There is no reasonable question to which 450 extra politicians is the answer.”
Labour said it supports the bill but will join Tory rebels to vote against a motion that would accelerate its passage through parliament. The party claims the government has failed to provide enough time to debate the legislation and may seek a national referendum on the issue.
However, Prime Minister David Cameron called Labour’s position “hopeless” and said he was confident that the bill would progress with the backing of cross-party support.
“We have been discussing this issue for 100 years, and it really is time to make progress. However, if those who support Lords reform do not get out there and back it, it will not happen.”
The government aims to have the bill on the statute book by early 2013, ahead of the first House of Lords election in 2015.