The bill was approved by a comfortable 225-vote majority when it was last debated despite the opposition of almost half of Conservative lawmakers.
But dozens of disgruntled MPs are expected to deliver a blow to Cameron's agenda by backing an amendment saying that if gay couples are allowed to marry, then heterosexual couples should also be able to have civil partnerships.
The main opposition Labour Party, while it backs gay marriage, has hinted that it could join the Conservative rebels, because it argues that the government has failed to make a convincing case against extending civil partnerships.
The delay would come because the government would need to work on the joint implementation of new rights for gay married couples and heterosexual couples in new civil partnerships.
Lawmakers are allowed a free vote on gay marriage, meaning they are not required to follow party directions, because it is considered an issue of conscience.
While Cameron, several senior party colleagues and his Liberal Democrat coalition junior partners back the bill legalising gay marriage, large sections of his party are fiercely opposed to the idea.
It comes at a time when Cameron is already under pressure from a large section of his fractious centre-right party over his stance on a referendum on Britain's membership of the European Union.
Grassroots Conservative supporters fear that with a general election two years away, Cameron's support for gay marriage is driving Tory voters to the UK Independence Party (UKIP), which had its best ever electoral performance last month when it made gains in local elections.
A letter signed by more than 30 current and former Conservative local association chairmen and handed to Cameron yesterday gave an indication of the bitterness felt by some in his party.
"You have failed thus far to keep the manifesto promise you made to recognise and incentivise marriage through a tax break for married couples," it said.
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