But his plan - details of which have not been made public - appeared to face long odds after the province's leading Protestant politician suggested some parts of the proposed deal were unacceptable.
"There's a large part of the document I could readily bring to the party. There are other elements that render the rest unworkable," said Peter Robinson, who leads Northern Ireland's Democratic Unionists, the province's major Protestant-backed party.
Northern Ireland has been transformed from the days in which the Irish Republican Army grappled with the British military and Unionist militias over the fate of the province, but lingering disputes over flags, parades, and how to deal with the legacy of the conflict periodically inflame sectarian tensions.
Haass, director of the New York-based Council on Foreign Relations and a former U.S. envoy to Northern Ireland from 2001 to 2003, was called in by the province's power sharing government to help resolve the issues. Six months of negotiations were supposed to have secured an agreement before Christmas, but even though Haass' deadline passed he said he saw enough potential to return for a second try.
The disputes that Haass has been trying to bring hinge on Catholic opposition to Protestant marches - long a trigger point for Northern Ireland violence - and the contested rights of both sides to fly their preferred British and Irish flags, an argument that has recently led to street blockades and clashes with police.
Both sides are also wrestling with the question of how to honor and bring justice for the 3,700 dead from the decades of bloody conflict.
In a statement to the press ahead of the last-ditch negotiations, Haass said more time wasn't the issue, giving the parties until Monday to come to an agreement.
"At some point we have got to fish or cut bait. That time has come," he said.