A number of backbench MPs in Cameron's Conservative party are expected to vote against the bill or abstain from casting ballots, CBC reporter Anne MacMillan said from London.
Reuters reports as many as half of Cameron's 303 Conservatives will vote down the bill. About 20 party members wrote to Cameron on Sunday, urging him to delay the vote and arguing that the party would lose significant numbers of votes in the next election as a result of backing it.
The Tories who oppose the measure say the essential purpose of marriage is to provide a stable environment for the care of children, and that happens best with parents of the opposite sex.
"A lot of older Tory supporters are being very vocal in their outrage about this," MacMillan said. "But when you look at opinion polls, 50 per cent say they're in favour, just 35 [per cent] against same-sex marriage."
Same-sex civil partnerships already legal
The bill is likely to become law because it is supported by Cameron, many members of his cabinet, and most Liberal Democrat and Labour lawmakers.
"The depth of feeling, love and commitment is no different between same-sex couples than opposite-sex couples," Culture Secretary Maria Miller said. "This bill enables society to recognize that commitment in the same way, too, through marriage."
Same-sex civil partnerships have been allowed in the U.K. for eight years. One of the more high-profile unions is between musician Elton John and his Canadian partner, David Furnish.
The bill would allow same-sex couples to get married in a town hall or a church, but would exclude clergy in the Church of England — the country's official faith — from having to carry out the ceremonies.
The bill allows for other religious groups that wish to conduct same-sex ceremonies — such as Quakers and liberal Jews — to do so if their governing bodies approve.
Same-sex marriage is legal in several European countries, including Spain, Portugal and the Netherlands. France is also taking steps to legalize it.
In 2005, Canada became the fourth country to introduce national legislation allowing same-sex marriage.