This agreement reached by Mrs Merkel and the leader of the SPD Martin Schulz could be rejected by the 460,000 members of the SPD at the end of February when they vote on the alliance.
The latest opinion poll of Insa has given the SPD just 16.5 percent of the vote.
The party’s membership will vote next week on the coalition deal struck last week between Mr Schulz and Mrs Merkel.
Opponents from the SPD to a new coalition have been campaigning under the slogan: “Join, and say no.”
Deputy party leader of the SPD, Ralf Stegner, has said: “We need a new start.
“The lack of discipline has to stop.”
Leader of the SPD group in Thurianga, Matthias Hey, said: “Our mood regarding what is happening in Berlin now is down in the cellar.
“We need someone to take charge of the bridge and start steering the ship”.
The new agreement between the two parties has seen the CDU give the SPD three prestigious ministerial posts of finance, foreign affairs and labour.
Germany, which is Europe’s biggest economy, has been without a government since September’s elections when Mrs Merkel failed to clinch a majority.
If the coalition agreement is approved, Chancellor Merkel should be elected the chancellor for the fourth term by the German parliament by mid-March.
The results of the ballot on the coalition deal will be announced on March 4.
This comes as the leader of the SPD Mr Schulz will hand over the role of leader of the SPD to Andrea Nahles.
The lack of leadership in Germany has caused concern among partners in the European Union which looks to Berlin for leadership in facing challenges from eurozone reform to Brexit.