On Monday the Alliance Party will reject DUP and Sinn Fein proposals to abolish the Department for Employment and Learning (DEL) and demand further negotiations.
The party may pull out of the Executive, not just the Justice Ministry, and go into opposition if it doesn't get a satisfactory outcome.
David Ford, the party leader, told the Belfast Telegraph a meeting of his party's ruling council would eventually be convened to decide "whether there should be Alliance participation in the Executive".
Mr Ford added: "The key question for the Alliance council will be 'is this enough for us to want to go into either the Justice Ministry or the Executive in general'."
The next scheduled meeting of the council takes place in March and, Mr Ford estimates, "it takes either two or three weeks to call a special one."
The proposal to abolish DEL was partly to reduce Alliance's ministries to the one it would be entitled under the d'Hondt share-out.
Abolishing DEL would require legislation. Mr Ford concedes that "given their numbers the DUP and Sinn Fein can push nearly anything they want through the Assembly, but that doesn't mean we can't challenge them", he said.
The prospect of Alliance leaving the Executive throws the calculations of the bigger parties into disarray, though some doubt that Mr Ford will follow through on the threat. This could lead to a lengthy impasse where both sides wait for the other to blink.
The problem is finding another agreed candidate for Justice. If Mr Ford refuses it the DUP and Sinn Fein could call Alliance's bluff by trying to find another cross-community candidate.