The conservative Merkel was set to hold talks with Guido Westerwelle, foreign minister and head of the Free Democrats (FDP), her new coalition partners, as well as Horst Seehofer, from her Bavarian sister party, the CSU.
Germany's new-look coalition, formed after Merkel's convincing election win in September, has experienced a torrid few months amid bickering over tax policy, Afghanistan and Turkey's admission to the European Union.
"The new coalition has got off to a very poor start, especially in tax questions," said Gerd Langguth, professor of political science at Bonn university and Merkel biographer.
Ordinary Germans appear to agree, with a strong majority - 61 percent - saying the new coalition has had a "bad start," according to a recent poll by independent opinion research institute Forschungsgruppe Wahlen.
Analysts said the main flashpoint at Sunday's talks would be fiscal policy, with the FDP, seen as a business-friendly party, demanding the government upholds a pledge for deep tax breaks from next year.
According to the Bild am Sonntag paper, Westerwelle has told Merkel this is "absolutely the core priority" for the FDP.
However, leading Christian Democrats as well as several state and local leaders say a tax giveaway now would be disastrous given the tattered state of Germany's public finances.
The recession in Germany, the worst since World War II, has blown a huge hole in the budget with the government estimating it will have to take on a record €85.8 billion of new debt in 2010.
Langguth said the planned tax breaks could be moved to a later date. "I expect compromises. For example, they might postpone the tax cuts," he said.
Ahead of the meeting, FDP economic policy expert Hermann Otto Solms said a postponement of the tax cuts until 2012 - a year before the next legislative election - would be acceptable.
"If the relief comes into force in 2012, that would correspond with the original demands of the FDP," Solms told the Tagesspiegel am Sonntag newspaper.
The new partners are also at loggerheads over the country's mission in Afghanistan, Turkey's EU accession and a new museum about the fate of ethnic Germans expelled from Eastern Europe after 1945.
The squabbling has taken its toll in the opinion polls. A recent Forsa institute survey showed that opposition parties enjoyed more public support than the coalition for the first time since the election.
Support has softened especially for the FDP, which lost two points.
Backing for the usually popular Merkel, the most powerful woman in the world for four consecutive years according to Forbes magazine, has also dropped sharply amid sniping from within her own ranks.
A Dimap survey on January 10 showed satisfaction with Merkel's performance had slumped to 59 percent, a drop of 11 points from the last time the poll was taken in December.
And the Forschungsgruppe Wahlen survey indicated that 52 percent of voters thought Merkel "was doing little to set the course for the government", compared to 37 percent who approved of her management of the coalition.