Arlene Foster last night appeared to be digging in her heels and refusing to step aside as the first minister designate in a move which could risk the future of devolution.
Senior DUP sources said Mrs Foster should reconsider her decision and not put her personal pride before what was best for "the party and the people of Northern Ireland".
Sources said they believed Sinn Féin wouldn't back down from its position of not forming a government with the DUP if Mrs Foster was nominated as first minister before the inquiry into the ash-for-cash scandal issued at least an initial report.
One DUP figure proposed a compromise move for Mrs Foster whereby she would accept another ministry in the new Executive with the agreement that she would step up and become first ninister after the inquiry.
"I think that is an entirely reasonable compromise which doesn't involve Arlene being humiliated," the source said. "It wasn't a good election for us, we can't ignore that.
"But this is a possible solution that I think Sinn Féin would go for and it would enable Arlene to regain lost ground."
Another high-ranking DUP source said that about a third of MLAs felt "angry and let down" by their leader. But he said that Mrs Foster had strong support from her deputy, Nigel Dodds, and from senior party advisers.
"Arlene is determined to brazen it out and that is putting the future of devolution in jeopardy. She was once an asset to our party but she is now a liability.
"It's all about self-preservation - 'me, me, me, me'. I believe that's a major miscalculation. Sinn Féin won't back down. Given their election result, they have no reason to do so."
The sources said that just because this was Sinn Féin's position, the DUP shouldn't automatically oppose it.
"If Sinn Féin says it's Monday, it doesn't mean it isn't Monday and we all insist it's some other day," he said.
"I believe that Arlene and the team around her are leading us into a terribly bad decision."
Yesterday, Mrs Foster said she was determined to remain as party chief and lead the DUP into talks with Sinn Féin.
Bring on the deal-makers. Time to knuckle down to business. To set Stormont functioning again? That, too, but there are more pressing matters to address than a provincial parliament in Belfast - another strand of discussion needs to be opened.