"We are in a serious situation because the question of the migration crisis evolved into a power question," German lawmaker Kai Whittaker told the BBC on Saturday.
"It could well be that at the end of next week we have a new situation… Probably a new chancellor."
The crisis stems from a revolt over Merkel's "open-door" migration policy, which she declared in 2015 to aid Syrian refugees.
Instead, it launched a surge of at least 1.6 million migrants from Africa, Asia and the Middle East into Germany and its European Union neighbors – setting off a cascade of housing, employment, crime and other problems.
The looming political showdown pits Merkel against Interior Minister Horst Seehofer, the leader of the conservative Christian Social Union (CSU) party.
On Monday, Seehofer plans to order German border guards to refuse entry to migrants who have already registered in other European countries.
That would mark a sharp departure from the EU's Schengen zone principle, which erases border controls like passport checks between member nations – an affront that Merkel has said she will not tolerate.
"This is a European challenge that also needs a European solution," she said Saturday. "And I view this issue as decisive for keeping Europe together."