Minority Leader of the Senate, Phillip Aduda, disclosed the ultimatum to press after a mass walkout by his colleagues.
Mr Machina is seeking legal redress following Mr Lawan’s attempt to claim the ticket after losing his bid for the party’s presidential slot.
The electoral body in a statement asked Mr Machina to go to court over his dissatisfaction with the refusal of APC to submit his name.
The senators are investigating corruption allegations brought against the former CJN by 14 justices of the apex court.
INEC will take the lion’s share of the blame if this democratic experiment dies.
Mr Machina was certified as the winner of the primary, but he still expects the ruling party to double down its plot to trade his mandate for the Senate President.
If confirmed, Mr Shehu would replace Elias Mbam, who resigned to pursue his gubernatorial ambition in Ebonyi.
Last week, the party sent Mr Lawan’s name to INEC as the candidate for Yobe North, even though he was widely known not to have taken part in the primary.
The Senate on Tuesday announced Philip Aduda (PDP-FCT) as minority leader and Chukwuka Utazi (PDP-Enugu) as the minority whip.
Mr Amadi said the group was alarmed at the efforts of some politicians and party leaders to undermine the provisions of the electoral law.