Merkel urged to quit as party leader

Chancellor Angela Merkel, who already faces the tough challenge of bringing on board two parties with big ideological differences, is also coming in for criticism from her own ranks after the CDU's worst voter share since 1949.

While Merkel's position as chancellor remains unassailable, calls have come from the CDU's right for her to quit as party leader.

"It's important for there to be new momentum, for the party to no longer be ruled from the chancellery," said Alexander Mitsch, who is chair of the new FKA right-wing grouping calling for the party to rethink some of its policies — in particular migration.

Read more: Far-right AfD's surge worries Muslim refugees in Germany

"There are a lot of good people in the so-called second row of the party who would be in the position to take over the party leadership," said Mitsch, who named Finance Minister Wolfgang Schäuble among his choices as possible contenders.

Greens foresee tricky 'Jamaica' talks

Even if she did stand down from her party role, Merkel would have her work cut out putting together the first three-way government since the 1950s, with the Social Democrats (SPD) appearing to have ruled out the possibility of governing as part of a "grand coalition."

Read more: Can the Greens and FDP join Angela Merkel in a coalition?

A "Jamaica" coalition made up of conservatives, Greens and the business-friendly Free Democrats (FDP) would require concessions across the board. There are gaping ideological divides between the two smaller parties in particular, on issues such as transport and energy production.

Greens co-leader Katrin Göring-Eckardt on Tuesday said she foresaw "complicated negotiations" and, while new parliamentary co-leader Anton Hofreiter said the Greens would approach negotiations with sincerity, he also stressed that forging a new coalition was not an automatic process.

There are already calls from within the party to take a more left-leaning approach as a counterweight to the CDU and FPD within the coalition. "In such a configuration, the Greens must be more left-wing," said Jürgen Trittin, who will be part of the Greens' 14-strong negotiating committee.

Robert Habeck, environment minister for the northern state of Schleswig-Holstein and also part of the committee, said he thought talks would be difficult, given the deep differences between the parties and signs that the CDU and the Christian Social Union (CSU) were tacking to the right.

Rightward pressure from Bavaria's CSU

The Christian Social Union, the Bavarian sister party to Merkel's Christian Democrats, is licking its wounds after its voter share in the southern state fell to a historic low of 32.9 percent. It's something that's also likely to add to the chancellor's coalition headache.

Read more: Merkel's Bavarian allies CSU threaten rightward shift

Like his counterpart in Berlin, CSU leader Horst Seehofer has faced criticism over the bruising loss of support — much of it to the far-right Alternative for Germany (AfD).

Still worse for Seehofer, there have been calls for his resignation. "We need another lead candidate for the state elections," said Alexander König, a member of the state parliament, on Tuesday. Seehofer's main rival within the party, Bavaria's Finance Minister Markus Söder, has kept a low profile since Sunday and says the immediate priority is to take note of grassroots feelings within the party.

What does look likely is that Seehofer will start to dig his heels in on major issues of disagreement with Merkel, especially migration. That could muddy the waters in coalition talks with the Greens, who want a more liberal approach to refugee policy and who have repudiated the notion of limits.

Petry to break with the AfD

After shocking those gathered at a press conference on Monday with the news that she would not join her party's parliamentary grouping, Frauke Petry — co-chair of the AfD and for a long time its public face — went a step further on Tuesday, saying she would quit the party.

Read more: Frauke Petry, co-chair of the far-right AfD, to quit the party

Petry, the highest-profile figure in the AfD's more moderate wing, has argued for the party to take a more moderate line. Her efforts have been frustrated, and she has clashed with senior members such as Alexander Gauland, who said the AfD would "hound" the new government and that Germany should be proud of its soldiers in World War I and II.

"We tried to change course but you have to realize when you reach a point when that is no longer possible," said Petry, whose husband Marcus Pretzell is also quitting the party.