Under fire over the inhumane treatment of immigrant children at the USA border, Trump is telling his supporters that an overly harsh treatment of illegal immigrants is surely better than the chaos Angela Merkel's open-door policy has created.
The two leaders will also have to settle on how to turn the euro zone bailout fund into a European Monetary Fund and complete a banking union Germany says is conditional on clearing non-performing loans from balance sheets. "It is pure disinformation".
For her part, Merkel has expressed optimism about her leadership and her ability to manage Germany through the tensions.
"We won't accept that the Schengen system is given up on the Belgian, Dutch and the French and Luxembourg western borders", said Armin Laschet, the conservative governor of Germany's most populous state, North Rhine-Westphalia.
If Merkel is given a two-week ultimatum, she would still have the Herculean challenge of persuading European Union governments to sign up to a common plan on the migrants. More than 1.6 million migrants, mostly Muslims fleeing wars in the Middle East, have arrived in Germany since 2014.
Matteo Salvini, interior minister in Conte's anti-establishment government that took office this month in Rome, has adopted a policy of blocking foreign humanitarian boats from Italian ports, which has triggered heated exchanges with France and the Netherlands.
Germany's interior minister insisted that his party has no intention of bringing down Chancellor Angela Merkel and her government, amid uncertainty Sunday over chances of a solution to a bitter standoff over migration.More news: Belgium fans hopes high at the 2018 FIFA World Cup
President Trump has repeatedly tried to pass off his administration's new "zero tolerance" policy of separating immigrant children from their parents at the border on Democrats, even as other administration officials have doubled down on the practice.
In turn, Merkel praised Seehofer's "master-plan" by calling the document "a good foundation" for resolving the existing migration policy issues.
Things came to a head last week when Merkel blocked his hardline plan.
If Seehofer, who has always been critical of the chancellor, decides to defy her, it could spell an end to the 70-year alliance between his Bavarian conservatives and those whom she represents in the remainder of the country.
Alternatively, if the CSU splits from the CDU and becomes an opposition party, the governing coalition would be left with 353 seats, one short of a majority, potentially triggering the collapse of the government.
Merkel would still have options if the CSU quit the coalition: Greens leader Annalena Baerbock refused on Monday to rule out replacing the CSU in Merkel's coalition.
However, in terms of substance, he showed no sign of shifting his position and other leading CSU members said they wanted to start implementing the policy quickly. The AfD that swept into Parliament previous year on a wave of anti-migrant sentiment is staging a march Sunday through the heart of Berlin to protest against the government.