The favorite to win is a leadership duo composed of Finance Minister Olaf Scholz and his running mate Klara Geywitz, who both support the center-left SPD staying in coalition with Merkel's center-right Christian Democrats (CDU) until 2021.
During the hustings, Ms Esken and Mr Walter-Borjans made clear that they are not prepared to remain in a coalition unless Ms Merkel's party give in to a series of high-stakes demands, including extra billions in spending on infrastructure and a hike in the minimum wage.
Challenging them is Norbert Walter-Borjans, a former regional finance minister, nicknamed Robin Hood for cracking down on tax dodgers with secret Swiss bank accounts.
For now, the heavyweights of the party on both sides have urged calm.
Its party congress is expected to decide by next week - on whether it will continue to support Merkel.
While Scholz and Geywitz strongly favored staying in the coalition, Walter-Borjans and Esken have sounded much more skeptical and advocated changes to the coalition agreement.
The general secretary of Merkel's Christian Democrats (CDU) said his party wanted to work with the new SPD leaders and that the parties already had a common basis to work from. SPD delegates are set to approve the leadership - elected via a party ballot that ended Saturday - at a party conference starting on December 6.
Walter-Borjans and Esken, though long critical of the coalition, said they won't make a precipitous exit.
"We have said clearly that this is about substance; we have said that we must do more on climate, we have said that there must be massive investment".
"We didn't let ourselves be nailed down to the question of everything coming down to the question of fleeing (the coalition) or staying in permanently", Walter-Borjans said. The two said they would be willing to leave the coalition unless Merkel's conservatives renegotiated their coalition agreement - something the CDU has rejected. "We stand by this coalition on the basis that has been negotiated".
The left-leaning TAZ daily said the SPD decision was a "solid vote of no-confidence against the party establishment".
Some have mentioned a snap election or a minority authorities may very well be on the playing cards.
Now, with the SPD having been junior partners in Merkel-led coalitions for all but four of her 14 years in power, many SPD members believe it is time to abandon the alliance to allow the party to regroup and rebuild its electoral base.
The far-right AfD also predicted an end of the coalition, with its co-leader Joerg Meuthen forecasting that "it will break up".
The coalition deal was struck only a year ago following inconclusive parliamentary elections in 2017.
In the latest opinion polls, the SPD, which came second in the 2017 federal election, is struggling for third place with the far-right AfD, behind the CDU and the Greens.