Her relations with the hard left and the SPD left have historically been atrocious. Arguably the Linke has better ideological reasons to oppose her than the CDU.
The SPD's first post-war Chancellor was the legendary Willy Brandt. He is most noted for a foreign policy paradigm shift of normalising relations with the East Bloc. Yet his undoing as chancellor was the unmasking of a high-profile East German spy in his personal staff. Brand's successor was Helmut Schmidt, from the party's right wing, both economically and in foreign policy (he used to be the SPD faction's hawkish foreign policy specialist), who prides himself of the behind-the-scenes instigation of the NATO Double-Track Decision that kicked off the eighties arms race (for details see this comment).
These two men continued to define the party into the Kohl era: Brandt remained party boss until 1987, while Schmidt became chief editor of liberal weekly Die Zeit and influenced a number of SPD leaders (including one youngster named Gerhard Schröder). Now Gesine Schwan was one of the latter: she was a founder of the SPD's right wing (the so-called Seeheimer Kreis = Seeheim Circle), an avowed Catholic, a vocal anti-communist and NATO supporter, and a loud critic of Brandt's line. But Brandt gained overhand by 1984, when Schwan wasn't re-elected into the SPD's policy-setting "Basic Values Commission", in practice ending her career as politician.
Still, two decades later, Schwan's relations with the post-communist PDS (one of the originators of the Left Party) weren't that frosty. In the 2004 vote for President, she lost to Horst Köhler 589:604 - presumably collecting the votes of all SPD (458), Green (90), Danish minority (1) and PDS (31) voters present (plus at least 9 right-wingers or liberals). And upon declaring her cnadidature in 2009, Schwan said (watch video in the Die Welt article):
Early in WWII, Köhler's ethnic-German family was deported from areas Stalin grabbed from Romania, and settled in the Polish village of Skierbieszów, which the Nazis cleansed of Jews. Horst Köhler was born there in 1943, and his family became refugees again the next year. They settled in Leipzig, but with the emergence of Soviet-controlled East Germany, fled on to West Germany.
Around the same time, Gesine Schwan's parents participated in the religious resistance to the Nazis that centered on the Lutheran Church (though her mother was a Catholic). In the last year of WWII, they were hiding a Jewish girl. *Traitor*, n. A benighted individual who perceives an illusory distinction between serving his nation and abetting the criminals who govern it.
