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“There will be a lot of CDU voters that want to avoid a grand coalition, and therefore swing over and vote for the Free Democrats,” Ms. Schroth said. “The FDP will benefit from the danger that it might not make the government.”

But she said it is “not clever,” because if too many Christian Democrat voters swing over to the Free Democrats, it would weaken Mrs. Merkel’s re-election chances. The plan backfired in a state election earlier this year, so her party will be wary of this.

“They don’t want them loaning votes anymore,” Ms. Schroth said.

Regardless of whether the Free Democrats stay in the government, it doesn’t necessarily mean Mrs. Merkel will continue working with them, said Mujtaba Rahman, head of the Eurasia Group’s European division.

In order to rule effectively, Mrs. Merkel needs to form a majority government of 50 percent or more, but that looks unlikely if she teams with the Free Democrats. In the TNS Emnid poll, they combined for just 45 percent.

This was not a problem in the latest election, when the Free Democratic Party received 14 percent of the vote, but support for the party has since dropped and it is polling only at 4 percent to 6 percent.

Instead, Mr. Rahman expects Mrs. Merkel to form a grand coalition with the Social Democrats, which means the two largest parties would work together in government, even though they have opposite political ideologies.

“The Free Democrats will probably get into the parliament,” he said, “but they won’t get a majority, in which case Merkel will turn to the Social Democrats.”

Despite the prospect of more years on the outside looking in, the Social Democrats are divided over the prospect of a grand coalition with Mrs. Merkel.

The party was part of the government during her first term, but many top officials are uneasy about playing second fiddle again to the dominant conservatives. Mr. Steinbruck has even said publicly that he would sooner leave the party than support this coalition.

That said, the Social Democrats could move on without Mr. Steinbruck after the elections. Many are betting that the Social Democrats will change their minds because the party would rather share power than be on the sidelines for another four years.

“I find it hard to believe that they would be unwilling to get in bed with Merkel,” Mr. Rahman said. “If they have a chance to be in government and in power, they will do that.”