Both blocs agreed late on Monday they needed more time to reach a deal on renewing their "grand coalition" and decided to resume talks at the headquarters of Merkel's party on Tuesday.
"Each of us will have to make painful compromises and I am ready for that," Merkel told reporters.
"When we see the movements on the stock markets over the last hours, we live in turbulent times and what is expected of us as popular parties... is that we form a government for the good of the people, one that brings stability," she said.
Merkel's failure to cobble together a government more than four months after the election has raised concerns among investors and partner countries at a time when Europe is facing multiple challenges - including the need for euro zone reform and Britain's departure from the EU.
Germany could face a new election or an unprecedented minority government if SPD members reject a coalition deal. But negotiators from both blocs said they must reach agreement on Tuesday.
Andreas Scheuer, secretary general of Merkel's Bavarian allies, said there was no possibility of extending the talks beyond Tuesday: "So we have to come to an agreement tonight. Anything else would be unreasonable for our citizens."
After initially vowing to rebuild in opposition, the SPD is now trying to extract concessions on healthcare and employment policy that could win over sceptics among its 443,000 members, who get the final say on whether to go ahead with the coalition.
The Rheinische Post newspaper reported that the Constitutional Court was examining complaints about the legitimacy of the SPD members' ballot. There was no comment immediately available from the court.
In 2013, the court rejected an injunction seeking to stop a similar ballot on the grounds that it was unconstitutional to give SPD members more say than other voters.