Elections in September left the veteran leader weakened and without a majority as some of her party's voters turned to the far-right AfD, angered by her liberal refugee policy.
The disputed decision to let in more than a million asylum seekers since 2015 is also proving to be a stumbling block as she seeks an alliance with an unlikely group of parties spanning the left and right of the political spectrum.
Merkel's conservative CDU party and its Bavarian allies the CSU have been trying to find common ground with the pro-business FDP and the Greens.
Party chiefs had initially set 6:00 pm (1700 GMT) Sunday as the moment of truth, but the deadline went by without a breakthrough -- the second overtime after already missing a previous target on Thursday.
Bild daily said on its website that "failure is in the air" while other German media were speculating that parties may call time-out to reflect on their options.
If talks collapse, Germany risks returning to the polls in 2018, as the centre-left Social Democratic Party has ruled out returning to a coalition with Merkel after suffering a humiliating loss at September's elections.
CDU vice-chief Julia Kloeckner urged negotiators to "pull together and get something done".
For Merkel, who has years of gruelling EU negotiations under her belt, this could be the most important weekend of her political life.
"Today is not only about (the coalition), but also a day of destiny for Angela Merkel. If she fails to forge a coalition, then her chancellorship is in danger," said Bild.
Frank Decker, a political scientist at the University of Bonn, had no doubt about what is at stake.
"It is absolutely in her interest for this government to come into being, because failure would spell her end," he told the Phoenix news channel.
A poll by Welt online found that 61.4 percent of people surveyed said a collapse of talks would mean an end to Merkel as chancellor. Only 31.5 percent thought otherwise.