There is no way that the Linke/PDS would be brought into the cabinet, but if a minority government were feasible in Germany, you maybe could have SPD+Green even if the two parties were short of the absolute majority.
On the other hand, while I found Schroeder's justification for early elections dubious - i.e. that due to dissatisfaction on the left of the coalition he didn't have a working majority, that would absolutely be the case with a minority govt. In practice I far prefer a right wing govt or a grand coalition than a left wing one that is largely powerless, and that's what a minority govt would be. The existing right wing veto power in the Bundesrat would be joined by a formalized far left wing veto power in the lower house.
I also think it could turn around and hurt the SPD (and Greens) politically as centrist and center left voters decide that they prefer a mainstream right wing coalition to a one combining the mainstream and extreme left.
I should have been more clear on what I was arguing. Of course, brainwave is right about the procedure that could elect a minority government. But then Schroeder would be openly dependent on the Linke. So the requirement for an actual election of the government in parliament means, in effect, you cannot have a minority government (even if it is not actually against the constitution).
This is very different from the situation in many other parliamentary governments where the cabinet takes office and is ASSUMED to have confidence until proven otherwise. That matters, in terms of political fallout, because such a government has not been openly put in power by a far-left party that most of the public disdains.
The parallel would be some of the past Scandinavian minority social-dem governments that have held power because the far left would abstain on a no-confidence vote called by the conservatives after the government was formally in office.
The theoretical reason is as I tried to articulate above: Sometimes parties may be willing to cooperate somewhat informally, but not if there must be a formal vote resulting in a public declaration of mutual dependence.
