Speculation mounted that the DUP leader, who was back at Hillsborough Castle for further talks with Sinn Fein and the British and Irish governments on Tuesday night, was struggling to convince the party to back a deal on the devolution of policing and justice and parades.
DUP Deputy Leader Nigel Dodds branded the reports as "pure fabrication and invention".
"There were no Assembly members threatening to resign from the Party. The meeting broke up with the unanimous decision that members were encouraged by progress and the negotiating team would seek to deal with outstanding issues," Mr Dodds said.
East Londonderry DUP MP Gregory Campbell said the party enjoyed a "healthy debate" over a range of issues within the Assembly group.
A DUP spokesman also added: "Peter had the unanimous support of the party yesterday to continue working to get the outstanding issues addressed.
"The DUP is holding out for the right deal."
'Leadership'
On Monday night, Mr Robinson emerged from the meeting with his party to say that he was not yet ready to sign-up.
"The (party) group has identified, because the negotiations have not been completed, some issues that have to be resolved and items about which they need to be satisfied," he said.
Peter Robinson however insisted his party wanted to see the devolved political institutions work.
Senior DUP sources told UTV they didn't expect a new party meeting to be reconvened before Wednesday.
"When Peter Robinson eventually does meet his assembly team, it's going to be a fairly key meeting", UTV's Political Editor Ken Reid said.
"This is a difficult period for Peter Robinson and the DUP leadership. Make no mistake about that."
"The debate was quite heated because this is a big issue. This is the final stage of devolution. Ultimately it is the test of Peter Robinson's leadership. He is likely to bring the bulk of his party with him. But he might have to take one or two casualties."
On Tuesday, Sinn Fein MLA Alex Maskey warned a deal needed to be concluded "quite quickly", after Sinn Fein leaders briefed party colleagues at Stormont.
"We are satisfied that a deal can be concluded, the deal needs to be concluded quite quickly and our focus is entirely on making sure the good work and progress that has been made in recent days can be built upon," he said.
SDLP leader Mark Durkan urged the parties to find agreement.
"You always have the big problem here that if things don't move forward, do they slide back?" he asked.
"Some of these issues are being treated as if they are the private property of the DUP and some of its more doubting members at that," said Mr Durkan of the current talks.
"It is not the best of way doing things, leaving things resting on the opinions of a few people inside one party."
Ulster Unionist leader Sir Reg Empey, who spoke to Prime Minister Gordon Brown and Peter Robinson, told UTV the deadlock illustrated the dysfunctional nature of the executive.
"All parties should have been negotiating. That's how you build confidence."
"It is hugely embarrassing to the government, hugely embarrassing to the Prime Minister and I think it is hugely embarrassing for Northern Ireland."
Downing Street said Gordon Brown was in regular contact with all the parties, as well as the Northern Ireland Secretary and the Taoiseach.
The spokesman said: "The parties are still talking and that is really important."
"No one ever thought this was going to be easy, but the fact is that the talks are continuing and the Prime Minister continues to follow the talks closely."