In Germany, there is always a procedure, and in this case, it is spelled out in the constitution, whose framers were obsessed with stability (for very good reasons). The new parliament will be convened on October 22, 30 days after the election. That is the constitutional maximum. With this first plenary meeting (parliamentary parties haven been holding business meetings since Monday), Merkel’s second term as Chancellor will end, and so will the tenure of her ministers. The Federal President will however ask her ‘to continue to manage Germany’s affairs’ until a successor is appointed, and she is obliged to heed that request. So are the ministers. There is no ‘gap': We’ll always have someone who tells us what to do.
The president will then go to parliament and propose a successor. But ‘then’ is relative. Interestingly, the constitution which is usually very precise, does not stipulate a time-frame. Leading commentators say the time-frame must be ‘appropriate’. Four weeks are ok. Six weeks would be ok, too, I think. But how much longer?
In theory, the president could come up with any proposal, but in practice, his suggestion has always been based on a viable coalition agreement between the parties, since his proposal must be confirmed by more than one half of its members (as opposed to more than half the members happening to be in the chamber at that point). The constitution is extremely wary of unstable majorities, let alone minority government.
Should the president’s candidate not be elected (this has never happened in the past), parliament has 14 days to make up their minds. During this period, they can elect anyone who manages to get the votes of more than half of the members without the president having any say.
Failing this, parliament will have one last vote on the Chancellor. Under this rule, the person receiving the most votes wins. If, by some happy coincidence, the number of these votes exceeds the number of half the members of parliament, the new Chancellor is sworn in and appointed. If it is less, the president has a choice: Within seven days, he can either appoint the Chancellor to lead a minority government or trigger new elections. Again, the choice is his in theory, but in practice, he would consult with the parties.
So where does that leave us?
Should both the Greens and the SPD refuse to join a Merkel government, they could still form a coalition with the Left or negotiate a toleration arrangement. But that seems unlikely, since the political costs would be very high, and it is not clear that all leftist MPs would vote for him. A small group of SPD and/or Green MPs could vote for Merkel to get on with it, without the parties entering a formal coalition, or one of the two parties could officially decide to tolerate her. As long as that would give her a majority in the inaugural vote, the president would have to appoint her. Or the parties could agree on having another election, with unknown consequences (AfD and/or FDP entering parliament, losses for all but the Left?).
Given these prospects, a CDU/SPD coalition will probably look like the lesser evil once everybody has calmed down a bit. But that might take some time.