The findings mean the SPD's place as one of the two main parties in Germany is under threat for the first time since World War II.
The SPD is currently holding a postal ballot of its 463,723 members on a coalition pact with Merkel. But the party is in chaos, riven by infighting over the deal.
Martin Schulz, its former leader, was forced to resign after losing the confidence of members.
The disarray has seen support for the SPD plummet, with a poll for the Insa Institute this week finding it had dropped to an all-time low of 15.5 per cent, behind the AfD, which moved into second place on 16 per cent.
Merkel's Christian Democrats (CDU) are still comfortably in first place, on 32 per cent, but she needs the SPD's support to form a new Government.
A militant campaign by opponents of the deal within the SPD, to sign up new members to vote No, recruited about 24,000 people before a deadline earlier this month. But that has now been undercut by the disclosure that one of them was a dog.