Senior Cabinet ministers have attempted to win over the wavering MPs in a letter to the Daily Telegraph that insists gay marriage is the "right thing to do at the right time"
Chancellor George Osborne, Foreign Secretary William Hague and Home Secretary Theresa May have questioned whether it was "any longer acceptable to exclude people from marriage simply because they love someone of the same sex".
Justice Secretary Chris Grayling also spoke out in favour - telling gay magazine Attitude it was a "sensible next step" in tackling homophobia in the UK.
"Changing a law has never automatically changed someone's opinion or belief, but a change in law can result in a more supportive and protective environment," he wrote.
Despite this, there is intense opposition to the move from Tory traditionalists from the party's grassroots all the way up to the Cabinet. However the Prime Minister will join the large majority of Labour and Liberal Democrat MPs in voting for the legalisation of same-sex marriage.
Some estimates put the number of Tory MPs against the measure at upwards of 150, including Environment Secretary Owen Paterson among other ministers.
All three main party leaders are allowing a free vote on what is seen as a conscience issue, although the programme motion for the timetabling of the Bill's passage through parliament is whipped and could serve as a test of the Prime Minister's authority.
In the joint letter published in the Telegraph, Cameron's three most senior Cabinet allies wrote:"Marriage has evolved over time. We believe that opening it up to same-sex couples will strengthen, not weaken, the institution."
"Attitudes towards gay people have changed. A substantial majority of the public now favour allowing same sex couples to marry, and support has increased rapidly. This is the right thing to do at the right time.
Mr Grayling said social acceptance of homosexuality over the past two or three generations had been "a real step forward".
"The Government's proposals on the recognition of gay marriage are a sensible next step in that evolution. They make it clear that the attitudes of today's generations are very different to those of the past.
"Of course we need to protect the right of the individual to have a conscience and of religious institutions to follow their own path. But that does not mean that the state has to do the same."
Nick Herbert: MPs Should Do the Right Thing on Gay Marriage
On Monday, Culture Secretary Maria Miller told The Huffington Post UK there was "there is absolutely no pressure" being placed on Tory MPs to back the measure, but said the government would not budge.
Labour leader Ed Miliband is expecting in the region of 25 of his own MPs to vote against the plan, although all of the shadow cabinet will support the Marriage (Same Sex Couples) Bill at its crucial Second Reading.
But the proposals - which are opposed by the Church of England and its new Archbishop of Canterbury Justin Welby - should still pass easily as they are backed by the vast majority of Labour and Liberal Democrat MPs.
Mr Miliband said he would "proudly" vote in favour and would actively urge his MPs to join him in making "an important step forward in the fight for equality in Britain".
Maria Miller: The Tories Are Progressive, We Ended Slavery
Making the case for gay marriage on the BBC's Today Programme, Labour MP Angela Eagle revealed how former Deputy Prime Minister John Prescott had reacted to her coming out in 1998.
"He asked if it was OK to give me a hug," she said."He said: 'Tell me something I didn't know already, love.'"
Legalising gay marriage would be "the final piece in the jigsaw," she said.
Ms Eagle, the Shadow Leader of the House, clashed with former Daily Telegraph editor Charles Moore, a staunch opponent of the plans.
The columnist said he was worried about the "destiny of the human race" and warned of "diluting" the concept of marriage.
He added: "I don't think it should be trivialised."
A poll last night suggested Mr Cameron's drive to legalise gay marriage could cost the Conservatives more votes than it wins.
More than one-third (34%) of those taking part in the ComRes survey for ITV News said it made the Conservatives less attractive to them as voters, compared to 15% who said it made the party more appealing.
Voters were divided over whether the coalition Government was right to try to make same-sex marriage legal, with 42% saying they were, against 40% who said they were not.
:: ComRes interviewed 2,050 British adults from February 1 to 3.
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