German chancellor Angela Merkel's centre-right coalition government looked to be close to collapse today, weakened by a string of disagreements and intense infighting over austerity cuts, policy reform and the departure of senior conservatives.

Less than eight months after it took office, the government was given only a narrow chance of running to a full term by the majority of Germans, 53% of whom said in a poll they expected it to fall.

"Either we get things sorted out in Berlin, or it will soon be the end for the coalition," said Jorg-Uwe Hahn, head of the Hessen branch of the Free Democrats (FDP), the junior coalition allies of the Christian Democrat Union (CDU) and its Bavarian sister party, the CSU. Renate Künast, leader of the opposition Greens, said: "The phrase 'new elections' is in the head and the heart of anyone who is thinking in a politically responsible way."

Merkel called at the weekend for the government partners to bury the hatchet over their disagreements after a week when relations reached such a low that members of her government had variously referred to each other as "wild pigs" and "gherkin troops" (rank amateurs).

But much of the mistrust and anger is being directed at Merkel herself. This week's Spiegel magazine called her the Trummerfrau, a reference to German women who cleared away the rubble after second world war bombings. It painted a picture of a woman presiding over a government in ruins and used its title page to request the government in one word to "Aufhören!", or stop.

Criticised at home and abroad for mishandling the euro crisis, Merkel's latest political headache is the four-year €80bn (£67bn) austerity package passed last week in an attempt to reduce Germany's deficit. Many of Merkel's own CDU MPs fear a voter backlash after growing criticism that the cuts are socially imbalanced. Almost 80% believe the cuts to be socially unfair, while 67% want an increase in the top rate of tax, which Merkel has strongly resisted. Public anger at the package spilled over at the weekend when thousands of demonstrators took to the streets.

The package has also stoked the anger of Merkel's French counterpart, Nicolas Sarkozy, who has accused the Germans of creating an atmosphere that will stifle growth in Europe at a time when it should be stimulated. Sarkozy arrived in Berlin for talks with Merkel tonight – a meeting which the German leader cancelled at the last minute a week ago, adding to speculation that relations between the two politicians are at an all-time low.

The recent departure of CDU heavyweight Roland Koch, the state premier of Hessen, and the unexplained resignation of Horst Köhler, another CDU man, from the post of president have also left Merkel looking increasingly exposed. Two further ministers have covertly expressed their desire to quit Merkel's government, including its most popular politician, defence minister Karl-Theodor Guttenberg of the CSU, who has faced a backlash over his attempts to scrap compulsory military service, and Philip Rössler, the FDP health minister, whose efforts to reform the health system have been rejected by parts of the bickering government.

The chaos has led commentators to refer to Merkel's administration as a "constipated institution". Writing in the Süddeutsche Zeitung, commentator Daniel Brössler said: "Governments need to be steered, but the Merkel cabinet is no longer steering. It resembles a car where the only thing that's working is the brakes."

All eyes are now on June 30, when politicians will vote for Germany's new president – either the Merkel-backed candidate, Christian Wulff, state premier of Lower Saxony, or the opposition-backed, East German-born Protestant vicar and human rights activist Joachim Gauck. A growing number of FDP politicians are pledging to support the pastor, snubbing Merkel. If Merkel's candidate loses, the common consensus is that the chancellor's position would become untenable.

She would then be likely to face a vote of no confidence in parliament – an event that has happened three times since 1949 – which could ultimately lead to a switch in coalition partners, or more likely, new elections.

The last coalition government to collapse before completing its elected term was the Social Democrat-Green alliance under Gerhard Schröder, which collapsed in 2005.

• This article was amended on 15 June 2010. The original refered to Karl-Theodor Guttenberg as a member of the CDU. This has now been corrected.