Interior Minister Horst Seehofer's CSU party at a meeting unanimously backed his call to give Merkel a fortnight to find a European deal on the burning issue by a June 28th-29th EU summit, failing which he would order border police to turn back migrants.
Three years after her decision to open Germany's borders to migrants fleeing war in Syria and Iraq and misery elsewhere, Merkel is still struggling to find a sustainable response to complaints from the CSU, her Bavarian allies, over her refugee policy.
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Merkel's woes come as European Union countries are once again at loggerheads over immigration, triggered by Italy's refusal this month to allow a rescue ship carrying 630 migrants to dock.
Malta also turned the vessel away, sparking a major EU row until Spain agreed to take in the new arrivals.
Seehofer has been one of the fiercest critics of Merkel's liberal stance, under which over one million asylum seekers have been admitted into the country since 2015.
He wants to turn away at the border new arrivals who have previously been registered in another EU country -- often their first port of call, Italy or Greece.
But Merkel says that would leave countries at the EU's southern periphery alone to deal with the migrant influx. Instead, she wants to find a common European solution at the EU summit in Brussels.
"How Germany acts will decide whether Europe stays together or not," Merkel told her CDU party's leadership at a meeting in Berlin, according to participants.
Popular misgivings over the migrant influx have given populist and anti-immigration forces a boost across several European nations, including Italy and Austria where far-right parties are now sharing power.
In Germany, voters in September's election handed Merkel her poorest score ever, giving seats for the first time to the far-right anti-Islam AfD.
Several high profile crimes by migrants have also fuelled public anger. They include a deadly 2016 Christmas market attack by a failed Tunisian asylum seeker and the rape-murder in May of a teenage girl, allegedly by an Iraqi.
With an eye on October's Bavaria state election, the CSU is anxious to assure voters that it has a roadmap to curb the migrant influx.
"We must send a signal to the world: it's no longer possible to just set foot on European soil in order to get to Germany," a leading CSU figure, Alexander Dobrindt, told the party meeting.
Seehofer had struck a more conciliatory tone, telling Bild on Sunday: "It is not in the CSU's interest to topple the chancellor, to dissolve the CDU-CSU union or to break up the coalition.
"We just want to finally have a sustainable solution to send refugees back to the borders."
'Almost a miracle'
Merkel now faces the challenge of persuading EU governments to sign up to a common plan on the migrants.
Central and eastern EU nations such as Hungary and Poland have either refused outright or resisted taking in refugees under an EU quota system.
A populist-far right government in Italy and the conservative-far right cabinet in neighbouring Austria have also taken an uncompromising stance.
Merkel's talks later Monday with Italian Prime Minister Giuseppe Conte in Germany could prove crucial if she is to have any chance of forging an agreement in Brussels.
On Tuesday, she will also meet French President Emmanuel Macron in Germany.
Berlin is also reportedly preparing to call a meeting between Merkel and the leaders of several EU frontline nations in the migrant crisis ahead of the EU summit.
"It would be almost a miracle if she emerges a winner from the next EU summit," Welt daily said.
But the chancellor may have no choice, as Seehofer could still launch the nuclear option of shutting Germany's borders in defiance of her -- an act of rebellion which would force her to sack him.
That "would be the end of the government and the alliance between CDU and CSU," an unnamed CDU source told Bild.