Stormont's five main political parties spent the weekend attempting to finesse a range of proposals from the Haass team in a bid to strike agreement before Christmas.
A massive push to seal a deal on handling contentious parades and dealing with the legacy of the Troubles by Christmas Eve is under way.
Talks chief Dr Richard Haass and his vice-chair Meghan O'Sullivan said they would leave "no stone unturned" in their efforts towards a breakthrough.
And they effectively told the five parties "it's over to you" after a plenary session yesterday.
But they also signalled there may be disappointment over the biggest sticking point – the flying of the Union flag. The DUP, Sinn Fein, Ulster Unionists, SDLP and Alliance will spend today working on the proposals, which have already gone through two drafts.
But they will be exchanging emails and possibly holding bilateral or multilateral meetings rather than hammering out the shape of a deal in the same room.
American diplomat Dr Haass and Harvard professor O'Sullivan will then draw up a third draft of their proposals late tomorrow.
Dr Haass said the document would then be made public fairly quickly, hopefully on Tuesday (December 23).
If agreement is close – but still elusive on the night before Christmas Eve – Dr Haass and Ms O'Sullivan will then decide whether it is worth resuming the talks the day after Boxing Day, December 27.
Dr Haass said: "We are getting close now to what we call in America crunch time.
"The assessment is there is time enough between now and Christmas to get this done."
But he also warned: "It is inconceivable that every party gets everything it wants."
He said that, possibly, there would have to be "some disappointment" over the flags issue.
The parties agreed to push on yesterday after first meeting the Haass team separately, when there were reports that some of the parties preferred to take a break and resume the talks again on December 27.
After earlier suggestions that there was little prospect of agreement in the talks before Christmas, the DUP left the hotel without further comment, but Sinn Fein was more upbeat.
Former junior minister Gerry Kelly said "our view is that we can crack this before Christmas", but his party wanted a comprehensive deal also including flags.
The Ulster Unionist Party said it had advised Dr Haass to 'park' the section of his report on flags – and return to the issue in the new year.
Leader Mike Nesbitt said sidelining flags would allow the parties to focus on parading and the past, over which his party still had reservations.
"We have a particular concern about dealing with the past.
"We have said repeatedly that we will not engage in or allow the rewriting of history. That part of the document could be a Trojan horse.
"It is about the rewriting of history and about the language which is being used or not being used," he said.
Alliance MP Naomi Long said "the only question is whether the will is there" to do a deal.
And an upbeat former SDLP Executive minister Alex Attwood said the decision to stay working over the 48 hours suggested that there was renewed intent in the negotiations.