The prime minister called on them not to "sit on their hands" and side with Jeremy Corbyn and others he labelled "a bunch of terrorist sympathisers".
Labour's leader has said bombing is not a sensible way to bring peace to Syria.
The BBC's Carole Walker said the PM wanted to win the Commons' backing without having to rely on Labour MPs.
Opposition leader Mr Corbyn was forced to offer a free vote to his MPs after a shadow cabinet rebellion.
As many as 50 Labour MPs could support David Cameron although party sources have suggested this number is falling as Mr Corbyn seeks to persuade them to listen to his arguments against intervention.
Meanwhile, thousands of protesters, led by the Stop the War coalition, have taken to the streets of London for the second time in four days to protest against bombing.
The government motion to be voted on would authorise air strikes "exclusively" against so-called Islamic State - also known as Isil or Daesh - in Syria, and says the UK government will not deploy troops in "ground combat operations".
It says military action is "only one component of a broader strategy" to tackle IS.
According to the BBC's latest research, of the 640 MPs likely to vote, 360 MPs are in favour of the motion while 170 are against. Of the remainder, 20 are "leaning to" supporting the government, three are "leaning against" while 87 are undecided.
SNP leader Nicola Sturgeon has confirmed her party's 54 MPs will be opposing air strikes, saying bombing on its own will not rid the threat of terrorism or bring peace to Syria.
The Liberal Democrats have confirmed that their eight MPs will support the government, with the Democratic Unionist Party saying its eight MPs will also back airstrikes.
Lib Dem leader Tim Farron has written to party members, saying he is aware many in the party will disagree with the "difficult" decision he has made, but he has done so because "the threat to Britain and our allies is clear".
He wrote: "I believe it is right to support what is a measured, legal and broad-based international effort to tackle the evil regime that has contributed to the hundreds of thousands of desperate refugees fleeing for their lives."
Addressing a meeting of the 1922 Conservative backbench committee, Mr Cameron warned that if Tory MPs voted against airstrikes they risked undermining a strong message that the UK was standing alongside its allies, including France and the US - already engaged in military action.
The PM's attack on Mr Corbyn - which mirrors comments he first made in his party conference speech in October - was criticised by one Labour MP likely to back airstrikes. Wes Streeting said it was "not the sort of thing" he expected to hear from the prime minister.
While in recent days the government has been trying to court Labour MPs, the BBC's Carole Walker said it was now apparent Downing Street was keen to carry the vote through a combination of its own MPs and their "natural allies", such as the DUP.
Mr Corbyn has urged Labour frontbenchers who support airstrikes to "think again", saying they are "not a sensible or rational way forward" and would "takes us yet again into another conflict".
In an interview with BBC political editor Laura Kuenssberg, he said MPs "must bear in mind what the public think and what the implications are for this country".
More than 75% of Labour members polled by the party had indicated they were opposed to air strikes, he said.
Asked about his failure to convince his shadow cabinet to back his position, he said: "Some people are more difficult to persuade than others, and I look forward to them being persuaded."
Rather than air strikes, Mr Corbyn said efforts should focus on a political settlement and achieving a "credible line of government" across Syria.
Asked whether, if he was prime minister, he would urge France and the United States - which are already bombing IS in Syria - to stop, he said: "I would ask them to put their efforts into a peace process."
He added: "I would ask them to join in looking for the way in which we can achieve a political solution to the Syria civil war as the best way forward of solving that problem."
MPs rejected air strikes against Syrian government targets in 2013, but have since backed strikes against IS in Iraq. Ministers say it is "illogical" to carry out strikes in Iraq but not Syria as IS does not recognise the border between the countries.
One of the key debating points has been Mr Cameron's claim there are 70,000 moderate ground forces able to fight IS in Syria.
The prime minister's spokeswoman said a claim by Labour MP Louise Haigh that the national security adviser had briefed MPs that 30,000 of the 70,000 were "much more radical Islamists" was a misrepresentation of what he had said.
Ms Haigh made the comment on Twitter, and was challenged by other MPs who had been at the briefing. She later insisted the government must "be clearer about the make-up" of the 70,000 figure.
David Cameron has urged Tory MPs to take a stand on fighting terror on the eve of a vote in Parliament on authorising UK airstrikes in Syria.