Fifty senior Tory activists are arguing the party risks alienating voters if it does not back same sex marriage.
An open letter, signed by leading grassroots members, urges Tory MPs to listen to the "wider views" of voters who support the plan.
On Sunday, 20 current and former local party chairmen warned the change could harm Tory electoral prospects.
MPs are to vote on legalising same sex weddings on Tuesday but a number of Tory MPs are likely to oppose the bill.
The Marriage (Same Sex Couples) Bill would enable same-sex couples to get married in both civil and religious ceremonies, where a religious institution had formally consented, in England and Wales.
It would also allow couples who had previously entered into civil partnerships to convert their relationship into a marriage.
The plans have been strongly backed by Prime Minister David Cameron, but he is facing significant opposition from within his own party.
Reports suggest upwards of 120 Tory MPs could vote against the plans, including some cabinet ministers.
MPs will have a free vote on the issue, meaning they will not be issued orders by party whips, but the measure is expected to get through, with most on the Labour and Lib Dem benches supporting it.
Downing Street said the prime minister had no plans to speak on the issue before the vote and there were no plans for him meet wavering MPs.
On Sunday, more than 20 current and former constituency chairmen delivered a letter to 10 Downing Street urging the prime minister to delay any parliamentary decision on gay marriage until after the next election.
It warned of "significant damage to the Conservative Party in the run-up to the 2015 election" if the plans enter law.
But supporters of the plan have hit back, with over 50 Conservative activists, including constituency chairmen, the chair of Conservative Future - the party's section for under 30s - and the chair of the National Conservative Convention - which leads the party's grassroots work - urging MPs to listen to the "wider views" of voters.
They warned that opposing gay marriage could "risk alienating the voters we will need in 2015", adding that a "substantial majority" of the public support the plan, particularly younger people.
The letter says: "Please do not allow the impression that all Conservative Party activists are opposed to gay marriage. Many of us strongly agree with the proposal.
"Nor is it true that gay marriage has no mandate. David Cameron made his support for it clear in his first conference speech as party leader, and won loud applause. It was in the party's equalities manifesto at the last election.
"We agree that there are many vital issues for the government to tackle. But marriage and how we treat minorities are important issues, too.
"We urge our MPs to listen to the wider views of their electorate as they decide how to vote."
'Issue of principle'
Geoffrey Vero, chairman of the Surrey Heath Conservative Constituency Association, who wants the bill to be delayed, told the BBC's Daily Politics it was costing the party votes, and some supporters were no longer prepared to help out with canvassing.
He said it was a complex area and called for a "much more rational discussion" and not for those opposed to be dismissed as "old fogeys".
Gavin Barwell, a Conservative MP who backs same sex marriage, said he believed in the institution of marriage and wanted as many people as possible to benefit from it, providing religious safeguards were in place.
He also dismissed fears that the issue could damage the party at the next election.
"It is an important issue of principle and the polling evidence suggests it is unlikely to have an impact one way or the other at the next election," he said.
The new Archbishop of Canterbury, the Most Reverend Justin Welby, who was confirmed in the role on Monday, said he stood by the Church of England's criticism of same sex marriage.
He said: "I have no idea how the vote will go, so I am not going to get into hypothetical questions.
"I stand, as I have always stood over the last few months, with the statement I made at the announcement of my appointment, which is that I support the Church of England's position on this."
He also warned that there must be "no truck" with any form of homophobia in any part of the Church.
In the bill, the Church of England and the Church in Wales will be banned from offering same-sex marriages because of their strong stated opposition, unless they change canon law. Other religious organisations will be able to "opt in" to holding ceremonies.