"It would begin with a humanitarian briefing."
This, my friends, is the legacy of the Myanmar debacle. Humanitarian briefings at the Security Council have become politicized, so now no one wants to have them, because from the briefing would come a press statement, then a presidential statement, and then maybe a resolution, maybe with sanctions. This is the road the US, UK, and France went down with Myanmar and Zimbabwe. Each time, China and Russia double-vetoed.
So now, nobody wants to talk about Sri Lanka, no matter how many people get killed.
The US and EU, at least, have announced their support for a briefing, and Amb. Susan Rice clarified the US position last week:
"The United States feels strongly about and concerned about Sri Lanka and we support the provision of it to the Council- a full and updated information on the humanitarian situation."
China, needless to say, is opposed.