The Prime Minister has said he is now "open-minded" about Britain taking some refugees. No 10 has signalled that agencies on the ground in the refugee camps are being asked to identify the most extreme hardship cases: children have been orphaned in the conflict and others have terrible injuries.
Unlike other European countries, the UK has thus far steadfastly refused to take any refugees, rather concentrating on leading the humanitarian assistance drive with taxpayers having pledged or given £600 million. It has also taken in more than 1000 asylum seekers.
But calls for the UK to do more are growing within Westminster, raising the prospect Mr Cameron will move in the next few days to avoid humiliating defeat if the Liberal Democrats side with Labour in the forthcoming Commons vote.
Sources close to Nick Clegg made clear the Deputy Prime Minister believes the moral case for taking in refugees from the Syrian civil war is "overwhelming" and that the LibDems had been arguing the case for weeks.
One senior LibDem source said: "The Coalition Government has been the most generous in the world when it comes to helping with the humanitarian crisis in Syria and it would be completely self-defeating to allow ourselves to be painted as the least generous.
"The Liberal Democrats will continue to make the case around the Cabinet table. We have yet to gain the agreement of our Conservative colleagues but we remain hopeful that we will."
Sir Menzies Campbell, the former LibDem leader, said: "The children of Syria have suffered grievously and disproportionately. Surely, we can find it in ourselves to admit as refugees those who have been orphaned, disabled or traumatised?"
Labour has urged the UK Government to take several hundred refugees. Douglas Alexander, the Shadow Foreign Secretary, told the Herald that Mr Cameron had failed to convince some on his own side of his decision not to take in some refugees.
He said that Labour would be "seeking to build cross-party support" for its motion between now and the vote.
Mr Alexander, who has visited Syrian refugee camps, added: "I hope in the days ahead we can get the Government to recognise the strength of feeling and argument that, complementary to the humanitarian work, there's more that can be done and should be done."
But Conservative backbencher Andrew Mitchell, the former International Development Secretary, said that while the PM was "absolutely right to look at some cases", allowing Syrians into the UK was "not going to resolve this catastrophic situation". The wish of the vast majority, he added, was "to return to their homeland".
More than 130,000 people are believed to have been killed in the Syrian conflict. Around eight million of the country's 22 million people have been driven from their homes and 11 million are in need of international aid.
The UNHCR - the United Nations refugee agency - is appealing for Western countries to resettle 30,000 of those trapped in the region around Syria.