The Greens, too, are pressed for time. Even before the first meeting of their parliamentary group yesterday, several Green MPs were offering urgent advice to a government that has yet to be formed. "There must be very quick decisions, to make it clear that things are changing in Germany," said Claudia Roth, one of the new MPs.
Ms Roth, a former member of the European parliament and a leading representative of the Greens' fundi wing, the so-called fundamentalists, is especially impatient with her future coalition partners' dithering over nuclear power. "We need to legislate for the closure of nuclear plants, and we need to make it quite clear that some of these plants will be closed down immediately," she said.
She was speaking to The Independent shortly before joining her colleagues in the first meeting of the parliamentary party since the elections. Green MPs had conferred on Monday night, but are split along fundi and realo - the so-called pragmatists - lines.
How the 47 of them will combine, and how they can co- operate with Mr Schroder's Social Democrats have become the central questions in German politics. The answers will define the speed of Mr Schroder's progress through the minefields of government.
The early signs do not seem encouraging. The Greens' leadership yesterday demanded four out of 16 cabinet posts, one more than expected. They put employment and a new nationality law at the top of their list of priorities, followed by the eco-tax on petrol, and nuclear power.
The latter looks set to provide the sternest test for the coalition-builders. On this issue at least, Mr Schroder is in no haste. The SPD has pledged to "phase out" nuclear power, maybe over 10 years.
It had been expected that, in the spirit of give and take, some minor concession will be tossed to the Greens, perhaps by setting an earlier deadline. Parliament is elected for only four years, so in some ways Mr Schroder can promise over a 10-year span whatever he likes. But if the Greens stick to their guns, some real compromise might have to be struck.
In judging what the Greens will buy, Mr Schroder is hampered by the fact that not even Joschka Fischer, the Greens' de facto leader, knows what can be sold to his members. Although they have come a long way from their organic vegetable patches, the Greens remain an unconventional party. So unconventional, that their membership sets the party line, and the leaders have to toe it.
The structure of the party is diffuse and painstakingly democratic. Genders have to be balanced in every post, as do the regions and the two wings. The fundis are nowhere near as dogmatic as their predecessors 20 years ago, but they try hard to live up to the label. Half the team of 12 that sits down to negotiate with Mr Schroder on Friday are fundis.
Even then, the Social Democrats might not discover the Green bottom line. Ms Roth thinks, for instance, that even if Mr Fischer becomes Foreign Minister, her wing of the party will not be entirely reassured. "Foreign policy will be difficult," she says. "We have different ideas concerning the Bundeswehr, and security structures in Europe." They want to abolish conscription and to water down Nato's role.
The fundis have other ideas, too. They will not scupper a coalition deal, because the Red-Green project is too important for all participants, but they are certain to apply the brakes to Mr Schroder's progress.