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Political leaders will resume talks at Hillsborough Castle later over a £2.5bn financial package aimed at restoring power-sharing government.
The offer from Westminster is contingent on the return of devolved government in Northern Ireland.
The Democratic Unionist Party (DUP) has been boycotting it since early 2022 due to its protest over post-Brexit trade arrangements.
The party has said there is still more work needed on the deal.
There had been speculation an agreement was close, with the government hoping to restore devolution before parliamentary recess on Tuesday.
However, DUP leader Sir Jeffrey Donaldson told members on Saturday that he would not be "distracted by hype" and "calendar-led initiatives".
Writing in an email, he said the financial package did "not deal with our long-term challenges" and that he was hopeful the government would "advance on their offer on Monday".
On Sunday, Sir Jeffrey also hit out at the Traditional Unionist Voice (TUV) after posters appeared across Northern Ireland saying "stop DUP sellout".
He said the party was behind the posters and said he would not be intimidated. In response, the TUV said posters are not intimidation.
What will the parties be discussing?
The government's offer includes a lump sum to settle public sector pay claims and a new "needs-based" funding formula for public services.
Party leaders in Northern Ireland have agreed that the current financial offer is not enough.
Monday's discussions will involve the four parties eligible to form a power-sharing government if it is restored - Sinn Féin, the DUP, Alliance and the Ulster Unionist Party (UUP).
Speaking ahead of the talks, Mr Heaton Harris said the parties have had time "to consider the generous package offered by the government".
"I look forward to discussing final details with the parties over the coming days."
The DUP has been urged by other parties not to hold up a potential return to Stormont and to "seize the opportunity" to restore devolution.
Speaking on BBC News NI's Sunday Politics, Sinn Féin's John Finucane said Sir Jeffrey needed to show leadership.
"What's clear this week is that there has been momentum," he said.
"It's clear that the time is now for Jeffrey Donaldson not to waste that momentum.
"If he prevaricates and allows this to drift then that will be to the detriment to everybody in this society."
Political leaders return to Hillsborough on Monday to talk money, still not knowing if they will be in a position to spend it.
The government had hoped to be making plans for re-establishing Stormont after receiving the green light from the Democratic Unionist Party (DUP).
Instead we got a leaked email from its leader Sir Jeffrey Donaldson to party members making it clear they are not over the line yet.
It did feel like a party preparing for government when it feels the time is right.
Most of the email was directed at the ongoing battle to get more money from the Treasury.
But there is a frustration the DUP leader appears to be stalling for more time and wants the process parked until after Christmas.
Read more from Enda here.
Any possible restoration of Stormont also depends on key discussions about the Windsor Framework and how Northern Ireland trades with Great Britain.
On Wednesday, Prime Minister Rishi Sunak said the government was ready to legislate to protect Northern Ireland's position and would work "at pace".
Sir Jeffrey said on Saturday he had been able to identify "legislative measures and potential actions that would be in keeping with our negotiating objectives".
But he said they would be "measured against the tests in our manifesto, and that work for Northern Ireland and our place within the United Kingdom".