After the election in September, SPD leader Martin Schulz ruled out another "grand coalition" with the conservatives.
German taxpayers may also be unimpressed by another promise in the new coalition agreement which declares that Germany is "ready to contribute more to the European Union budget".
CNN says the agreement "represents a U-turn by the SPD, which had originally said it would rather rebuild itself in opposition than prop up another Merkel administration, after suffering its worst election result since World War II".
Ms Merkel made heavy concessions to the Social Democrats (SPD) after breaking more than four months of political deadlock to agree to form a coalition government - including handing over the powerhouse Finance Ministry.
"The way in which Schulz left could make it hard to quickly focus on the party's achievements in the coalition talks", Carsten Nickel, a Brussels-based analyst at Teneo Intelligence, said in an e-mail response to questions. It looks unlikely to hit trouble there, despite discontent over the party losing the finance and interior ministries.More news: Katy Perry is letting go of 'childhood trauma'
Meanwhile Alice Weidel, the head of the far-right AfD's group of MPs in the new parliament, criticised the coalition's proposed immigration policy, which would see up to 220,000 asylum seekers given residency each year and a scheme to encourage highly-qualified people to move to Germany. However, the deal can still be scrapped by the SPD's members, who will vote on the treaty with the outcome expected in early March.
Kuehnert, 28, is travelling around Germany urging members to vote against the deal.
Whether the coalition will actually materialise is still contingent on a vote by the SPD's approximately 460,000 members. The paper cited Friedrich Merz, a former CDU rival whom Merkel sidelined after becoming party chairwoman in 2000, as saying the coalition deal was a "humiliation" for the Christian Democrats.
Merkel faced an uphill struggle to maintain power for another four years following a disastrous election campaign.
But before she can be sworn in, a final hurdle looms: the hard-fought pact between her CDU/CSU bloc and the Social Democratic Party must still be approved by the SPD's skeptical rank-and-file.
After a failed attempt to forge an untried alliance with two smaller parties, Merkel opted to woo back the reluctant SPD-her junior partner for two of her three terms since 2005.