Earlier this month, as he prepared to give one of the most important speeches of his political career, Chancellor Olaf Scholz of Germany appeared before Parliament in a suit that appeared at least a size or two too large.

It was an apt metaphor. Mr. Scholz has never seemed a natural fit as chancellor. He was an unlikely selection to lead his Social Democratic Party four years ago. Now, his popularity has sunk, his government has broken up, and Mr. Scholz finds himself fighting for his political life.

With a snap election looming in February, some in Mr. Scholz’s party have begun to entertain what would be an almost unheard-of development in German politics: dumping their incumbent chancellor in favor of a more charismatic leader, in hopes of scoring a come-from-behind victory and remaining in power.

The discussions among party members — and the news media — have early echoes of the push in the Democratic Party to encourage President Biden to end his re-election bid amid mounting voter concerns about his age. Mr. Biden eventually stepped aside, and his replacement on the ballot, Vice President Kamala Harris, lost in November to former President Donald J. Trump.

Mr. Scholz still appears likely to hold on to his place atop the Social Democratic Party ticket. Unlike Mr. Biden, no one in his party has voiced concerns over his fitness to lead the country for another four years. Party leaders will decide who stands as their chancellor candidate, and for now, they are publicly standing behind Mr. Scholz.

But two weeks after Mr. Scholz ended his three-party coalition by firing his finance minister, leading to rare snap elections and political uncertainty in Europe’s most powerful country, his fate is uncertain. Every other party has formally designated their top candidate for the Feb. 23 federal election.