If Merkel holds firm and Seehofer does quit, the CSU could offer a replacement interior minister if it aims to remain tied to her party.
German Chancellor Angela Merkel reached a compromise deal Monday on migration with her rebellious interior minister, Horst Seehofer, to defuse a bitter row that had threatened her government. The deal, partly agreed to by Merkel to avoid divisions in her party, still must pass a series of approvals - from the Social Democrats, the other part of Merkel's coalition.
Seehofer, who has demanded that Merkel toughen her open-doors refugee policy, told colleagues on Sunday that in spite of the measures agreed with European Union leaders, he saw no alternative to turning some migrants back at the border.
"For the Christian Social Union (CSU) it is of utmost importance not to lose its credibility.The promise has been that Seehofer would stop immigration of those who are not entitled to go through the asylum procedure in Germany". However, the current dispute has erupted as Germany is seeing far fewer newcomers than in 2015.
It was the latest aftershock from Ms Merkel's 2015 decision to open Germany's borders to more than one million refugees fleeing from war in the Middle East and Africa. On Sunday, Ms. Merkel's party passed a resolution backing her stance.
Merkel has not resolved the underlying tensions in her coalition.
Only once before has the cooperation been at risk - in 1976 when Bavarian leader Franz Josef Strauss thought the CSU would fare better in elections if it were free of the CDU.
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Alternatively it could break up the two parties' decades-long partnership, depriving Merkel of her majority in parliament and pitching Germany into uncharted political waters. But in comments to the Sueddeutsche Zeitung newspaper, he complained that he was in an "inconceivable" situation. "This is a political mission to prevent turbulence in Germany and so it will be pushed through as such", said one senior European Union diplomat. Any migrant who already applied for asylum in another European country would be rejected and asked to return to the countries where they made the applications.
However, the more conservative CSU believes its credibility is at stake as it tries to curb support for the rival anti-migration Alternative for Germany party in the Bavarian election.
German Minister of Foreign Affairs Heiko Maas of the SPD said the crisis had already damaged the country's standing as a bulwark of European stability.
"So I think action in Germany to strengthen European interests is absolutely necessary", he said.
The centre-left Social Democrats, another partner in the coalition, must also accept the deal along with neighbouring Austria. The CDU's leaders, who are now gathered in Berlin for a second straight day of discussions, said they still see room for a compromise solution in the migration dispute.
"The blame game between CDU and CSU must end, because it is irresponsible", she said.