Each day now brings more erosion, more unraveling of the government of West German Chancellor Helmut Schmidt.

After months of wear and tear, the Bonn coalition -- at 13 years old, Western Europe's longest-surviving government -- is faltering and could collapse within the next two months.

Fighting to hold on against discouraging odds, Social Democrat Schmidt has started showing open irritation with his partners, the small Free Democratic Party, as they hint more strongly about a leap to the conservatives.

On the stump, Deputy Chancellor Hans-Dietrich Genscher, the Free Democratic leader, has taken to speaking of a "new majority" in the land. Still, Genscher has approached a breach in the past. But Economics Minister Otto Lambsdorff, a Free Democrat known to favor a swing to the right, virtually divorced himself from the coalition's budget principles this week with a bombshell memo to Schmidt that showed a strong neoconservative bent.

Lambsdorff's 34-page memo fiercely attacked federal budget compromises -- painfully negotiated up to now with the Social Democrats -- as "too shortsighted," too unsystematic and sometimes contradictory.

Arguing that previous austerity efforts had failed to restore business confidence, Lambsdorff proceeded to list as candidates for future cutbacks nearly every social program favored by Schmidt's party. He warned that unless radical steps were taken now, West Germany's political system could be endangered.

The paper infuriated Schmidt and was regarded privately by aides as a provocation intended to breach the coalition. Speaking to his party's parliamentary group today, Schmidt said Lambsdorff's radical proposals stood in "flagrant contradiction" with the coalition's economic and social policy.

In remarks reported by a party spokesman, Schmidt described the memo as displaying "an astonishing lack of analytical ability in an economics minister." The chancellor called the minister's report incomplete, one-sided and disappointing, adding that some parts of it must be seen by workers as "a provocation."

The Social Democrats' elder stateman and party chairman, former chancellor Willy Brandt, told the same meeting it was odd that Lambsdorff had not thought of resigning, given that the minister no longer stood by government policy and appeared determined to render the coalition powerless.

Brandt, who as chancellor in 1969 ushered in the current era of German detente and generous social welfare benefits, said in a despairing radio interview last weekend: "I am not optimistic about the future of the social-liberal coalition." While recalling that his party has a mandate to stay in office until the next scheduled elections in 1984, Brandt added: "I fear the train is already slowly moving in the other direction."

While the new tensions arise partly from a sharper clash over economic principles between the coalition's two parties, a conflict aggravated by West Germany's prolonged recession, much of the problem has to do with worried calculations by Free Democrats about political survival. Many liberals are now persuaded that continued association with the confused, increasingly less popular policies of the Social Democrats would mean their eclipse as well.

The next seven weeks provide a sequence of political trip wires widely expected to trigger the government's breakup -- although even at this point, nothing of how events will unfold is certain. At the same time, constitutional and political factors favoring an incumbent chancellor could result in Schmidt's completing his term.

A first test comes in Hesse state elections Sept. 26. Officials from both governing parties can be seen each evening campaigning there on rival platforms. The Free Democrats there have already broken with the left-leaning Social Democrats and hope to form a new coalition with the Christian Democrats -- Schmidt's main opposition nationally

If the Free Democrats in Hesse can keep their heads above the 5 percent cutoff for representation in parliament -- and if the conservatives are denied a majority, thus forcing the creation of a new coalition -- then the Free Democrats' confidence in precipitating a change in Bonn as well will be bolstered.

The excuse in any case for breaking with the Social Democrats could come in the second half of October when coalition talks on revising the 1983 budget are due to begin. Bleaker economic forecasts that emerged over the summer scuttled a narrow budget compromise in July.

On Nov. 5, the Free Democrats gather in West Berlin for a national convention that is bound to confront the coalition question -- if a new alliance has not formed by then.

Lacking the trust and cohesion anymore to take major initiatives, both coalition parties have fallen back publicly to shoring up their own positions, as if preparing for a place in history that will lay the blame for an eventual rupture on the other partner.

"If a historic epoch of the Federal Republic of Germany is to be broken off here," declared Schmidt in a challenge in parliament last week, "this should be done openly and with a clear declaration of will on the part of those who want this -- and with a justification that will hold in the face of the history of our state and not with the trivial, artificial, make-believe arguments that we have heard so far." The German leader said local election results were no basis on which to alter a coalition that has a federal mandate to govern.

Indeed, the Free Democrats are worried about being accused later of toppling Schmidt without convincing cause. He is still the most popular politician in the country.

In the highly emotional Hesse campaign, Social Democratic speakers regularly attack the liberals for vacillating between political camps for the sake of retaining power. In a country that values loyalty and steadfastness in its politicians, the charge of opportunism carries a particular opprobrium.

It is clearly a fine line between being an ally to the Social Democrats in Bonn and their adversary in Hesse that the Free Democrats are walking. The skillful Genscher, in his campign appearances, has avoided attacking the Social Democrats outright, but it is not difficult to read between his lines.

He has been declaring, for instance, that the way must be freed for a "sensible economic policy" -- a line that tends to get him lots of applause, according to those who have traveled with him. He does not say this is no longer possible with the Social Democrats, but he does not have to.

"Debts that are made today must be paid back tomorrow," he will say, a statement that any German audience knows is meant to align the liberal party chief, and Bonn foreign minister, with the conservatives.

But even a number of fellow Free Democrats expressed shock at the drastic scope of Lambsdorff's plan. A rowdy session of the party's parliamentary group failed to endorse the proposals, referring them to a committee for further discussion. The minister, reacting to today's comments by Schmidt and Brandt, said that he was not one to quit when the going gets rough.

Leading West German papers are now saying that the daily spectacle of the coalition battling itself is a wearisome, terribly costly experience for the nation and cannot go on.

For much of the public, the prospect of the government's falling carries little of the excitement conveyed by bold newspaper headlines. Rather, the drawn-out political grind -- this is the third time in a year Genscher has come close to switching -- has produced a sense of fatigue and pained impatience with it all.

National polls have for months shown voters, distressed with the coalition, moving away in two directions. Some have gone to the right, where the Christian Democrats have been polling over 50 percent lately. Others have shifted left to the radical but dynamic Green Party, which is drawing about 10 percent in the polls, several percentage points more than the Free Democrats.