The election result itself, in this north German city-state, the smallest of the country's 16 states, is unlikely to be a surprise.
The half-million-strong port city has been run by the left-wing Social Democrats (SPD) for the past 66 years, and opinion polls predict that the current SPD-Green coalition government will be returned to power.
The regional election - the fifth of seven in Germany this year – could nevertheless further hurt the standing of Chancellor Angela Merkel's federal government.
Her conservative Christian Democrats (CDU) are likely to be pushed into third place, while the pro-business Free Democrats (FDP), her allies in the federal government, are likely to fail to clear five percent and lose all their seats in the regional assembly.
Recent opinion polls suggest the SPD will win between 36 and 37 percent of the vote, the Greens 24 percent (16.5 percent in the 2007 election).
The CDU will likely get 19 to 20 percent (25.6 percent in 2007) of the vote, while the FDP will score between three and four percent (six percent in 2007), below the five-percent threshold needed to win representation, according to polls by the ARD and ZDF public television channels.
The far-left Linke party, a loose-knit grouping of former East German communists and disaffected Social Democrats, which first won representation in western Germany in 2007 when they took 8.4 percent of the vote in Bremen, this time stands to win between six and seven percent.
At the national level, the FDP is credited with three percent support, while the Greens have moved into second place with 26 percent of voting intentions, just behind the conservatives who are backed by 32 percent of voters, according to a Forsa poll released Thursday by Stern magazine and RTL television.
The poor showing for the FDP, which won 14.6 percent in the September 2009 general elections, is all the more galling as the party has just chosen a new leader, Philipp Rösler, who as a result has been promoted to economy minister and vice-chancellor.
Forsa chief Manfred Güllner suggested in Stern magazine that the party's continued low showing resulted from the fact that Rösler, the 38-year-old former health minister, is not considered to have sufficient experience to replace the outgoing 68-year-old economy minister, Rainer Brülerle, who now heads the FDP parliamentary faction.
In elections this year, the FDP failed to win seats in two state elections and was very nearly routed in a third.
The Greens, in comparison, have gone from strength to strength, helped in part by worries over nuclear power in the wake of the Japanese nuclear power plant disaster.
In March, they even led the polls to wrest power from the CDU in Baden-Württemberg, where the conservatives had governed for nearly six decades.
The Greens made their best showing ever, winning over 24 percent of the vote, a score which allowed local leader Winfried Kretschmann to become the first ever Green premier in a state government.
In Bremen, "the Greens should also score a victory on Sunday," said Gerd Langgruth, a political scientist in Bonn.
Not only will the ecologists be riding high after their previous successes, but the town is home to a large student population and surrounded by ever more unpopular nuclear power plants, he said.
In addition, "parties in power (at the federal level) traditionally tend to do poorly in regional polls held between general elections," he said.