"It was right when Martin Schulz proposed Andrea Nahles take over the interim leadership", Malu Dreyer, the influential regional prime minister of Rhineland-Palatinate said. They say it is against party rules and one of the current deputies should step in until members can vote on a new leader. The SPD is in a hard situation after its support fell to historically low levels after September's parliamentary elections.
The SDP's former leader said the coalition agreement was "70 percent" Social Democratic policy and encouraged party members to bring "the personnel debate to an end" with his resignation and concentrate on passing the deal.
The upheaval at the top of the SPD has distracted from party leaders' attempts to convince party members to agree to the coalition deal.
Schulz, 62, ditched plans to take the post of foreign minister after fierce criticism from some former allies, not least because he had pledged not to serve in a cabinet with Merkel.
"I will defend the idea of joining the big coalition, I will do all it takes to achieve this, "said Nahles, whose party, however, disagrees about joining a new large coalition of conservatives".
Schulz on Friday then gave up plans to become German foreign minister, hoping to shore up support among SPD members for the new coalition - but the manner in which he anointed Nahles as his successor rankled with many in the party.More news: Carlos Carvalhal: Swansea put 'all the meat in the barbecue', says manager
The planned handover of the SPD leadership from Martin Schulz to Andrea Nahles is also viewed with skepticism, according to a survey by Emnid for Sunday's edition of the Bild newspaper.
Schulz's decision to accept the post of foreign minister has also irked the incumbent, his party colleague Sigmar Gabriel, who called the move "disrespectful" on Thursday evening.
With many SPD rank and file harboring misgivings about sharing power with Merkel again, the result of the vote, due on March 4, is wide open.
Just 33 percent of German citizens said the SPD would be more successful under Nahles, while 52 percent did not expect this to be the case.
Germany has been without a formal government since the September 24 election and investors are anxious about a delay in policymaking, both at home and in the EU.
Nahles said she would start campaigning at the weekend for members to vote "yes" to a coalition with Merkel, who has led the European Union's most populous country and economic powerhouse since 2005.