A UUP MLA has told the BBC that a party meeting on the budget will examine "defining decisions" on whether its ministers should vote against it.
The meeting comes as criticism of the draft budget deepens, with only the DUP, Alliance and Sinn Fein explicitly giving it their backing.
UUP ministers Danny Kennedy and Michael McGimpsey have joined SDLP minister Alex Attwood in not endorsing it.
Mr Attwood has complained that it fails to serve those in greatest need.
However the biggest divisions have come between the health minister, Mr McGimpsey, and some of his executive colleagues, particularly the First Minister and Deputy First Minister.
Mr McGimpsey has been pushing for more funding amid a stream of controversial revelations about the heath service.
BBC NI political correspondent Martina Purdy said that the public tensions between Mr McGimpsey and his colleagues was a sign that executive discipline is breaking down ahead of the final vote on the budget on 14 March.
"The fact that the assembly will be dissolved soon after for elections makes it easier politically for the SDLP and Ulster Unionist ministers to reject the budget," our correspondent added.
"But such a scenario would certainly cause an almighty row between the coalition partners."
The draft budget, announced in December, is intended to save £4bn by the end of 2014-15.
It has been criticised from several sources, including a PWC report which called it a "patch and mend" approach and the Stormont finance committee which said it should have been completed much sooner.