BERLIN (Reuters) - Opening a crunch week that could prove fatal to Germany's tottering government, a senior party ally of Chancellor Olaf Scholz said he was optimistic of finding a budget agreement with the three-party coalition's wayward finance minister.

Christian Lindner, leader of the neoliberal Free Democrats (FDP), surprised his more left-wing coalition partners on Friday with a budget document that proposed tax and spending cuts and deregulation as the answer to Germany's economic malaise.

Both his coalition partners, themselves at odds on a host of issues, agree that targeted government spending is needed to stimulate the economy and reject the supply-side focus of the FDP, the smallest coalition party.

But Matthias Miersch, secretary general of Scholz's Social Democrats, said he expected all parties would live up to their responsibilities and find a way through the crisis.

"I'm optimistic that all parties want to create stability for this country in difficult times," he told public television on Monday.

"Supporting the economy, spurring investments and cutting bureaucracy: We share the same goals."

Germany would especially need a stable government if Donald Trump won this week's U.S. presidential election, he added, without elaborating.

Scholz, who met with his party's top leadership and dined with Lindner late on Sunday, is expected to hold talks with the Greens' de facto leader, Economy Minister Robert Habeck, on Monday, laying the ground for several three-way summits of the government's top leadership.

The three parties are at odds over a response to the structural headwinds facing Europe's largest economy, whose car industries are dealing with labour tensions and a growing competitive threat from Chinese rivals.

Habeck proposed an investment programme that would repurpose the 10 billion euros ($10.9 billion) freed up by U.S. semiconductor giant Intel's decision to back out of a government-backed chip factory project. Lindner would cut that budget allocation entirely.

Underscoring the tensions, the three parties have each held separate business dialogues in recent days.

"The German government has just entered a new stage of a slow burning political crisis that could be the last step before the eventual collapse of the governing coalition," wrote ING's Carsten Brzeski.

A collapse could leave Scholz heading a minority government until scheduled elections in September 2025, relying on ad hoc parliamentary majorities to govern, or to early elections, which polls suggest would be devastating to all three parties.

The SPD and Greens are both well down from their showing in the 2021 general election, while the FDP could be ejected from parliament altogether.

The conservatives, on 36%, are at more than twice the level of their nearest rival, the far-right Alternative for Germany on 16%.

($1 = 0.9181 euros)

(Writing by Thomas Escritt; Editing by Ros Russell)