French Polynesia's once dominant Tahoeraa Huiraatira Party is reportedly due to lose another assembly member to the breakaway Tapura Huiraatira group.
The president, Edouard Fritch, says Rodolphe Jordan has been in talks with his camp and is about to join.
A switch would give Mr Fritch's side the support of 28 members in the 57-strong assembly, which is one short of a majority.
Last week, Charles Fong Loi was the latest politician to quit the Tahoeraa which splintered after its long time leader, Gaston Flosse, last year lost the presidency because of a corruption conviction.
Flosse was however confirmed as party leader by the court last month when it ruled that the loss of civic rights was no impediment to remaining in charge of an association or a party.
Mr Fritch has said if he fails to secure a majority to pass the budget he would consider his work done and possibly have the government quit and the assembly dissolved.