For those having trouble following this, the SPD are socialists, but there is a further left party that came out of the ex-Communists in the east, but now incorporates the more Leftist parts of a splintered SPD.
The Ypsilanti woman needed the support of this far left party (as well as the Greens), but her own SPD refused that support, saying they would rather be in opposition than govern with the far left.