The discord within her conservative bloc burst into the open when Interior Minister Horst Seehofer of Merkel's Bavarian allies CSU hastily cancelled plans to present his “masterplan” on immigration.
The interior ministry said in a short statement that the presentation had been pushed back because “several points still need to be agreed”.
Seehofer, the former premier of conservative Bavaria state, has long been one of the fiercest critics of Merkel's decision to open Germany's borders at the height of Europe's migration crisis in 2015.
The migrant influx has shaped German politics since. Voters handed Merkel her worst ever score in September's elections as well as giving the far-right AfD seats for the first time in the Bundestag.
With a crucial state election in Bavaria coming up in October, Seehofer and his Christian Social Union party are anxious to stop a haemorrhage of support to the anti-migrant and Islamophobic AfD.
The CSU's strategy is underpinned by Seehofer's 63-point immigration plan, anchored by the key proposal to push migrants back across the border.
Standing his ground late Monday, Seehofer stressed that all 63 points of his plan “are in my view necessary in order to restore control and order in Germany.”
He added that he would not “publish a half-baked plan with lazy compromises.”
Underlining what is at stake, broadcaster Deutschlandfunk said if no deal is found, “the choices there for the interior minister would be resignation or dismissal.”
“That of course, would be the end of the coalition,” it added.
'They must be turned back'
The arrival of more than a million asylum seekers, many fleeing war-torn Syria and Iraq, since 2015 has deeply divided Germany.
Three years after the migration crisis erupted, the inflow has slowed dramatically but the coalition is still bickering over what would be a sustainable solution.
Within Merkel's CDU party too, some are openly championing Seehofer's vision.
“The masterplan is important now and it must be implemented quickly,” said Saxony premier Michael Kretschmer.
“Of course they must be turned back at the border. That's why we have police at the border and it is right to have them there,” said the CDU politician.
But Merkel won't accept turning refugees back, as it would simply shift the problem to Germany's neighbours.
Germany must not act “along individual national lines,” she said.
For the chancellor, the only sustainable solution would be a Europe-wide agreement.
That is a point she will likely push when she meets later Tuesday with Austrian Chancellor Sebastian Kurz, whose country would be hardest hit if Germany were to close its doors.
Ironically though, Kurz shares Seehofer's criticism of Merkel's refugee policy and is due to meet the interior minister on Wednesday.
Merkel has the backing for now of the third party in her coalition, the Social Democratic Party. It too rejects stepping up border controls of asylum seekers, which it says goes against the spirit of the Schengen passport-free zone.
'Wait for reform'
But the refugee influx has not only influenced electoral decisions in Europe's biggest economy. It has also pushed voters to the arms of populists and the far-right in Austria and Italy.
Signalling increasing frustration with new arrivals, Italy's far-right Interior Minister Matteo Salvini flatly refused to allow a rescue vessel carrying hundreds of migrants to dock on Monday.
Demands from the populist and far-right leaning forces are complicating Merkel's push for EU solidarity in dealing with immigration issues. The issue is to be covered at a summit on June 28 and 29.
With Austria taking over the rotating presidency of the EU on July 1, Merkel is hoping to convince Kurz to sign up to a system of “flexible solidarity” and help put in place an effective European border police.
EU budget commissioner Guenther Oettinger of Merkel's CDU called on Seehofer for patience.
“It would be good if Germany waits to see what the reform of the Dublin rules in Brussels brings, before it takes one-sided measures,” he told newspaper group Redaktionsnetzwerk Deutschland, referring to regulations surrounding asylum-seeking procedures in the bloc.