Some 460,000 members of the SPD are holding a referendum on whether to back a hard-fought accord for a government with the conservatives.
The results to be announced on Sunday morning could either end a political stalemate in the country five months after inconclusive elections, or sink it into deeper crisis.
In an interview with German broadcaster RBB-Inforadio, the party's general secretary Lars Klingbeil said he expected that “we will get a 'yes' on Sunday'”.
Hours before the postal vote closed on Friday, another leading member of the SPD warned the rank-and-file against torpedoing the deal.
“It would be bad for Europe, Germany and the SPD,” Stephan Weil told Welt daily, adding that it would open up a “period of political instability”.
The make-or-break vote for Germany's next government will essentially also determine Chancellor Angela Merkel's political future.
If the yes-sayers prevail, Merkel would begin her fourth term in mid-March.
But if the SPD rejects the deal, Europe's biggest economy probably faces snap elections that could hasten an end to Merkel's leadership after 12 years in power.