Part of the proposed political deal is "unworkable", Northern Ireland First Minister Peter Robinson said.
Mr Robinson said: "There's a large part of the document I could readily bring to the party, there are other elements that render the rest unworkable.
"I hope he (Dr Haass) will be able to see a conclusion and we're still optimistic it can be reached, but it won't be reached by us fudging issues or doing something more abruptly than we would otherwise want to."
Dr Haass has warned the individual parties will not get all they want and difficult choices will have to be made but the alternative to agreement had been seen in recent trouble on the streets.
"We hope this opportunity is seized, as time does not work in anyone's favour," he said.
"The last year has shown that flags and parades have the potential to further inflame an already divided society.
"Time also works against the ability to capture the past, as memory fades, as evidence is lost and lives end."
Sinn Fein Deputy First Minister Martin McGuinness told the BBC: "I just think that for Richard Haass and (vice chair) Meghan O'Sullivan to leave here without making an agreement would be a terrible embarrassment for politicians, for the process, and would clearly show a lack of leadership qualities in terms of facing up to these very difficult challenges."
A Historical Enquiries Team (HET) of detectives was set up to investigate unsolved Troubles murders, but has run into controversy after an inspection accused it of treating security force killings differently from those by paramilitaries.
All parties agree that the views of victims should be integral to any process for dealing with the past, but it has been difficult to decide what that mechanism should be and whether limited immunity from prosecution should be offered to those who give information about shootings, bombings and other atrocities.
The issue of where and when flags fly is likely to be left to a separate process as parties have been unable to reach a common position.
Parades meanwhile, are usually connected to the Orange Order, and while most are peaceful, a minority which pass through nationalist residential areas can prove controversial as some of those residents find them offensive.