Each head of state or government has his or her own way of telling their fellow world leaders that they get it -- that they all now have the same view, that the scientists have been borne out, and that the clock has run out, that agreement on a common global battle has to come now, and that the children would condemn us all if the agreement fails.
For weeks, observers have said it unlikely Obama, who arrives here Friday, and 130 other world leaders would all agree to travel to this summit without strong assurance of a deal.
As the on-again-off-again negotiations lurched into the night, many of the negotiators were found in side rooms scattered around this immense convention center -- which is now coated with a layer of new fallen snow.
News also filtered to journalists working late of high-level, but private, dinners in different precincts of Denmark's capital city.
Many negotiators, working on details of wording for some sort of global political agreement, expected they might get little -- or no -- sleep before Obama arrives.
World leaders have long called for America to take the lead against global warming -- and have taken heart from Obama's insistence, from the moment he took office, on giving it highest priority.
But at the last hour, despite so much agreement on the severity of global warming, it's still not clear what kind of a deal would be ready for him to sign.