In recent days that pressure has taken the shape of calls from the Liberal Democrats and Labour, and campaign groups like Save the Children, to open Britain's doors to 3,000 children, alone and potentially in danger on the migrant trail in Europe.
Today, just hours after the PM was accused of a "disgraceful" tone towards those in need, calling them a 'bunch of migrants', the government has given a partial answer to its critics.
There will be more cash and support for aid agencies to provide help for under 18s who are already caught up in the chaos and travelling across Europe.
The government is also open to resettling more child refugees in the UK. But they have stopped short of accepting more of those who are already in Europe, maybe even just across the Channel.
Instead, they are echoing the decision they took in the summer and may  allow more refugees under 18 to come here directly from the war-torn areas around Syria. Crucially, the government won't put a number on how many extra children will be allowed to come.
Sources indicate that the number will not significantly increase the current commitment to resettle 20,000 refugees from the region over the next five years. There was even discussion inside government over whether the overall number should increase at all.
There has been nervousness in government about the precedent it would set to take many more refugees from Europe, that could encourage more people to make the dangerous journey in the first place.
But the fact that the government has shifted its position at all displays how the demands of this crisis are affecting political decision-making here.
And just as the tempo picks up in David Cameron's testing renegotiations of our relationship with the rest of the European Union, the government's attitude to dealing with migration is in sharp focus. Ministers fear a backdrop of a seemingly chaotic migration on the continent could make their deal-making, and the eventual referendum campaign, even harder.
The prime minister has been under pressure, just as in the summer months when the full scale of the migrant crisis became clear, to make more effort to help the most vulnerable among the hundreds of thousands of people on the move.