The veteran leader, in power since 2005, won a September 24th vote without a clear majority for her conservative CDU/CSU bloc, largely because of the rise of the far-right Alternative for Germany (AfD), and must now build an unlikely alliance with the pro-business Free Democrats (FDP) and left-leaning Greens.
But their deep policy differences, especially on immigration and the environment, have hobbled the monthlong negotiating marathon, leading party leaders to miss a Thursday deadline and declare they will push on until Sunday evening.
Until and unless the motley crew of four parties, which spans the mainstream political spectrum, strikes a deal, Germany's government remains in effective limbo with Merkel serving as a caretaker chancellor.
If they fail, Germany would probably hold snap elections, which would leave Merkel increasingly exposed to a rising band of critics within her own ranks and could further bolster the anti-Islam AfD.
"There is the will to ensure that this political task succeeds, but it cannot succeed at any price," warned Alexander Dobrindt, a member of the CSU, the Bavarian party allied with Merkel, after arriving for the talks.
"Sunday at 18:00 (17:00 GMT), it's over. This weekend, we must decide," said FDP leader Christian Lindner.
In an interview with Die Welt newspaper, German President Frank-Walter Steinmeier called on the four parties to act responsibly in order to avoid a new vote.
Merkel, no longer deemed invincible after her poor election result, "now faces the most difficult task of her leadership so far," judged the Sueddeutsche Zeitung daily.
'Hanging by a thread'
Hours after a 15-hour red-eye meeting ended at around 4:00 am Friday, Merkel, the veteran of countless all-night EU summits, said that "the task of forming a government for Germany is so important that the effort is worthwhile".
Horst Seehofer, the embattled leader of the CSU, said that "we have the goal of finishing by Sunday" because the German people had the right to know whether or not a new government could be formed.
Looming over the political drama is the prickly issue of immigration, a hot-button topic since Merkel threw open German borders in 2015 to a mass influx of over one million asylum seekers.
While the CSU has been sharply critical and wants to cap future arrivals at 200,000 a year, the Greens argue that more refugees should be allowed to bring their families.
Deep differences also remain on climate policy, where the Greens want to phase out dirty coal and combustion-engine cars, while the conservatives and FDP emphasise the need to protect industry and jobs.
The Greens face a party congress in a week's time, where rank-and-file members will give the thumbs up or down on the concessions their leaders may have wrested from the other parties.
'Merkel's fading star'
Martin Schulz of the centre-left Social Democrats (SPD) -- Merkel's former junior coalition partner that went into opposition after a stinging election loss -- reemerged to criticise the painful process.
He charged that the four parties were searching for the "lowest common denominator" in an atmosphere of "maximum mutual distrust", led by Merkel, whom he labelled the "world champion in vagueness".
Schulz also charged that the odd alliance would diminish Germany's role in the EU and contribute to the "paralysis of Europe".
The Frankfurter Allgemeine Zeitung daily commented that, despite the hurdles, "Merkel can't afford to fail, because the SPD... won't come to her rescue again".
The smaller parties, it said, "are already fighting at the expense of the chancellor, who won't necessarily get the credit if the talks succeed, but who will certainly be blamed if this experiment fails".
Fresh elections would heap pressure on all parties, the broadsheet added, but especially on the chancellor "because then Merkel's star will fade even more quickly, maybe even for good."
By Frank Zeller