Losing Bremen, the country's smallest state with a population of just 680,000 people, would represent an earthquake for the party that has held it for 73 years. No other German state has been ruled by the same party for so long.
"Bremen is small but the psychological impact of this election is big," said Kevin Kuehnert, the leftist leader of the SPD's youth wing JUSOS who has caused an uproar by suggesting firms such as BMW should be collectivized.
Elections to the European Parliament take place on the same day and could pile further pressure on the coalition.
A lackluster SPD showing could be the outcome for a junior coalition partner that has consistently failed to take credit for its achievements and which leaves Merkel to enjoy the limelight on the international stage.
But for some, such as Kuehnert's supporters, it would be a clear call for change and a more left-wing agenda in opposition.
"There is too much complacency. We need a change - the SPD have done alright but it's been too long. They need time out - here and nationally," said teacher Jochen Lang at a sausage stand in a car park where the Greens, SPD and CDU campaigned.
A reluctant SPD was effectively forced last year to re-enter a Merkel-led coalition by the president after talks on a three-way tie-up without the center-left party collapsed at a time when support for the far-right AfD was surging.
Last year, a row over migrant policy nearly brought down the coalition and SPD chief Andrea Nahles acknowledged she had made a mistake over the fudged ousting of the domestic spy chief.
The party will review its role in the coalition at the end of the year, after three more state elections in the former Communist East, and the party is divided over whether to stay. Nahles wants it to carry on and said on Tuesday that the grand coalition "is not threatened by any result".
But defeat for quietly spoken Bremen leader Carsten Sieling, 60, may well cause many members to call time and could eventually trigger a snap election laden with risks for both the SPD and the chancellor's conservative bloc.
The timing of Merkel's exit has been a subject of increasing speculation since she handed the leadership of the CDU to protege Annegret Kramp-Karrenbauer last year.
"(Nationally), the SPD needs to go into rehab but it missed that opportunity when it went into government," said Gero Neugebauer, politics professor at Berlin's Free University.
"Although the coalition mood isn't good, they won't leave it lightly as they are nowhere near ready for an election" he said.
With unpopular Nahles looking weak, there is not even an obvious candidate to stand for the chancellorship.
The race in Bremen, whose strong commercial and industrial base has been hit by the decline of shipyards on the river Weser and the North Sea Bremerhaven port is going down to the wire.
The SPD is on 25%, down from 32.8% in 2015, and 1 percentage point behind the conservative Christian Democrats (CDU) and its new face: successful IT businessman Carsten Meyer-Heder, who has a big smile and easy manner.
The city is redeveloping its economy, turning to new sectors such as logistics and technology, while Mercedes and Airbus factories plus suppliers provide more than 15,000 jobs.
Bremen has the highest unemployment rate of any state, 9.7% compared with 2.8% in Bavaria, although rows of terraced houses are well kept and millionaires reside in stylish villas on the other side of the city that shares its name with the state.
Sieling pins a large part of the blame for his woes on the national party.
"We see in Bremen the problem of the weak position of the SPD nationally," Sieling told Reuters in the town square.
Nationally, the SPD is languishing at about 17% in polls, below the 20.5% hit in the 2017 election which was its worst result since 1933. Merkel's conservatives are at about 29%.
At 19% in national polls, the Greens are compounding the SPD's problems. The party may end up as kingmaker in Bremen.
With slogans like: 'Sieling: Governs Bremen Competently', the mayor is banking on locals opting for a safe pair of hands.
He is also proud of integrating some 15,000 migrants in the 2015-2016 crisis. Bremen is the only state not to have had a single attack on a refugee home, he said. The far-right Alternative for Germany (AfD) is relatively weak, at about 8%.
Unlikely to be able to continue his SPD-Greens coalition, many in the SPD hope Sieling may forge the first three-way tie-up of the SPD, Greens and radical Left party in western Germany.
But the CDU's Meyer-Heding is confident of victory.
"For the first time there is a chance for change and that's motivating people. This is a last bastion for the SPD. If they lose, it will send a very strong national signal," he told Reuters.