As state elections in Bavaria underlined on Sunday, Ms. Merkel’s personal popularity conceals a high degree of political fragmentation. That could make it tricky for her to assemble a governing coalition, especially if her center-right Christian Democratic Party performs the way polls suggest, winning this Sunday’s national election but falling short of an outright majority.

Her current coalition partner, the Free Democratic Party, did so poorly in the Bavarian election that it might emerge from the national vote with no seats. That could force Ms. Merkel, who is seeking a third term, to make a power-sharing deal with the main opposition party, the more left-leaning Social Democrats.

Meanwhile, pop-up parties — notably the anti-euro Alternative for Germany — have occupied political space vacated by Ms. Merkel as she moved left on issues like a national minimum wage and nuclear power.

The situation underlines the major role that small parties can play in German politics and the growing willingness of German voters to switch from one party to another.

“It used to be that 30 percent of the voters would vote for the Christian Democrats no matter what the party said or did,” said Stephan Werhahn, a grandson of Konrad Adenauer, the country’s first postwar chancellor.

“Today the voters orient themselves according to their personal interests,” said Mr. Werhahn, a Munich lawyer who himself defected from the Christian Democrats to a minor party last year but then returned this year. “The parties have had to take over more issues that are not in harmony with their basic principles, in order to attract these voters.”

German politics are still much more orderly than in some other European countries, like Italy and Greece. Still, Germany’s level of voter unrest is puzzling given that the country has not suffered nearly as much from the euro crisis. Unemployment here is near record lows.

“The situation in Germany is still very different from Italy or Greece, which are really under strain,” said Thomas Harjes, chief economist at Barclays Germany. He said some voters might feel a sense of powerlessness in the face of global forces that breeds disillusion with mainstream parties.

No party has felt the new fickleness of voters more acutely than the pro-business Free Democrats, long a fixture in the country’s postwar politics. Just four years after winning almost 15 percent in the national vote, they are at risk of falling short of the 5 percent needed to field a delegation to the national Parliament.

If they do fail, Ms. Merkel may need to form a so-called grand coalition with the Social Democrats. She could then have to balance their left-leaning demands with the right wing of her own party, which is already grumpy about her support for euro zone bailouts, even as citizens of receiving countries have excoriated her insistence on austerity.

Some of her disgruntled party members have even defected to Alternative for Germany.

One is Karl-Georg Glehn, a lawyer from Cologne who was one of several hundred people in Frankfurt on Saturday to attend an Alternative rally in front of city hall. “We’re liable for billions from the Greek economy, which is bankrupt, cronyistic and corrupt,” he said. “They would be better off with their own currency. Merkel is silent on all these problems.”

Alternative for Germany is the wild card in Sunday’s elections. It fielded no candidates in Bavaria, but its voters are regarded as highly committed and likely to vote, and polls show the party could come close to winning enough votes nationally to get seats in Parliament.

“I have a feeling there is an undercurrent of sympathy that is being underestimated,” said Christian Meurer, a political satirist and author of a recent book, “The Wackos Who Are Governing Us” (“Die Irren, die uns Regieren”).

Seats in Parliament would give the Alternative party a soapbox in Berlin and allow it to play a disruptive role in debates about European policy, while making it harder for Ms. Merkel to muster a majority. “The headlines these debates will generate will be very harmful,” said Mr. Harjes, the economist.

Ms. Merkel will also have to contend with the Christian Democrats’ sister party, the Christian Social Union in Bavaria, which is feeling its oats after a commanding victory last Sunday. The party, which normally does not field candidates outside Bavaria, won enough votes to form a state government by itself. Predominantly Roman Catholic, it is more conservative on many issues than the Christian Democrats, and will probably demand a substantial number of cabinet posts as payment for Bavaria’s support in Parliament.

In a sense, the Free Democrats’ unexpectedly strong showing nationally four years ago, when they won 14.6 percent, wound up contributing to their steep decline. Despite holding several cabinet posts, they were unable to deliver promised tax overhauls — Ms. Merkel preferred to focus on cutting debt. And Free Democrat leaders fought among themselves.

“It was our own fault,” said Jörg-Uwe Hahn, the minister of justice in the state of Hessen, who is also a member of the Free Democrats’ national governing body. “On the core issue, taxes, the party didn’t deliver quickly and decisively enough.”

Mr. Hahn said, though, that he was optimistic the Free Democrats would win the 5 percent of the national vote needed to get into Parliament. When the party has been in trouble in the past, Christian Democrats often crossed over to make sure it could be a coalition partner.

Karl-Heinz Paqué, an economist who was formerly leader of the Free Democrat delegation in the Saxony-Anhalt State Parliament, said it was inconceivable that the party would be excluded from national politics.

“The F.D.P. is part of German history,” he said.