Such an outcome would increase pressure from the SPD's rank-and-file for the party to pull out of the coalition with Merkel in Berlin.
Projections showed Mrs Merkel's conservatives heading for an extremely lacklustre win in the vote for the central Hesse region's state legislature. Although the CDU has remained relatively united behind its leader in public, discontent has been building as the party's fortunes have sunk.
Hesse's conservative governor, Volker Bouffier, complains that "the election campaign has been completely overshadowed by Berlin". "People want less fighting and more actual work done", he said.
The SPD won 20 percent, down from 30.7 percent in 2013, and pipped the ecologist Greens, on 19.5 percent, into third place.
Nor did the veteran leader's fourth government get off to a good start after its formation earlier this year, with two rows over relatively minor points bringing it to the brink of collapse over the summer. Back in 2013, the CDU had to make a coalition with the Alliance 90/The Greens after the election resulted in no clear victor.
Increasing numbers of SPD members are calling for the party to quit government immediately and lick its wounds in opposition, as it is presently polling below AfD nationwide, at 15 percent to the far-right's 16 percent. That's three times its tally from 2013, the year it was created. In the past Merkel has always said that the position of chancellor and the head of the party should be held by one person.
The CDU has governed Hesse for almost 20 years, and the party campaigned on an enviable record in the state of ultra-low unemployment, high wages and minimal crime.
Such results would make various regional coalitions possible, with the Greens potentially joining parties to their right or left or even, if their results are exceptionally good, having a chance to make their local leader Tarek Al-Wazir - now Bouffier's deputy - the state governor.
Possible contenders include Health Minister Jens Spahn, who has publicly criticized her open-doors refugee policy and is championed by the CDU's social conservatives; Ralph Brinkhaus, a fiscal hawk who unexpectedly ousted Merkel's longtime parliamentary caucus leader; and Annegret Kramp-Karrenbauer, her hand-picked party general secretary who's often cited as her most likely successor.
"By passing the baton of her own free will she would show that she knows the same thing everyone knows: the end of her chancellorship is approaching". Despite her party's historically poor result, she may be heaving a huge sigh of relief, too. Her party has been hammered in a regional election and battered in national polls. "Considering the circumstances, we can say that it's a clear mandate to lead the [Hesse] government", he said.
Merkel's predecessor, Gerhard Schroeder, stepped down as leader of his center-left Social Democrats in 2004 as his government struggled, but remained chancellor until he narrowly lost an election 18 months later.
However, the SPD's historic losses could mean yet more pain for the chancellor's already troubled government coalition in Berlin.
But such a move, triggering a collapse of the government, would nearly certainly lead to a snap election.