Speculation is rife about who will succeed the outgoing defence minister, Adolf Ogi, in the cabinet. The decision, due when parliament re-convenes in seven weeks, could put a strain on Switzerland's 41-year-old power-sharing formula.
Few political events highlight the intricacies of Switzerland's political system as much as the resignation of Ogi, considered a liberal within the ranks of his Swiss People's Party.
An unwritten law agreed by the main political parties before the Second World War and amended in 1959 stipulates that the largest four parties are represented in the federal government according to their strength at the polls.
Due to this rule, dubbed the "magic formula", the Swiss cabinet consists of two members each of the Radical, Social-Democratic and Christian Democratic Parties, and one People's Party member.
When Ogi's replacement is elected by parliament, probably on December 6, members will face a stark choice.
They can either vote for another moderate member of the People's Party - a move which would annoy the majority of the increasingly right-wing party - or they can elect a politician who is more representative of the party. The latter choice would make life hard for the cabinet which seeks to take decisions collectively.
The choice arises now because over the past decade the People's Party, under the informal leadership of its billionaire figurehead and populist politician, Christoph Blocher, has increasingly become an opposition party in all but name. Ogi, however, had remained in the mainstream of Swiss politics.
Of the 14 names that the People's Party leadership tentatively put forward on Wednesday as possible candidates for the succession, all but three or four are considered hardline followers of Blocher and his Zurich-based party wing. Above all else, they are vehemently opposed to Switzerland joining the European Union - one of the cabinet's main goals.
The People's Party president, Ueli Maurer - who is also from Zurich - said the next People's Party cabinet member "should be truly representative of his or her party".
However, he left open the possibility of presenting two candidates to parliament on December 6 - the implication being that one would be a moderate who is acceptable to a parliamentary majority.
Leading politicians of the other three governing parties have ruled out the possibility of ceding Ogi's seat to a party hardliner.
"It won't happen", said Christine Beerli, a member of the Senate from canton Berne and leader of the Radical parliamentary group. "I know enough People's Party politicians who can fit the bill, meaning that they work constructively towards common solutions," she told swissinfo.
The People's Party can nominate one or more of its own candidates. But, equally, parliament may choose a member of the People's Party who is not on its list of nominees. Asked about the possibility, Maurer said that the party "would have to accept such an election as the result of a democratic procedure".
It therefore seems unlikely that Ogi's resignation will upset Switzerland's "magic formula" which has ensured political stability since 1959.
Only last weekend, the newly elected president of the Social-Democratic Party, Christiane Brunner, threatened to oust the People's Party from the cabinet altogether if it put forward a hardline right-wing nominee.
But Brunner on Wednesday ruled out torpedoing the "magic formula".
"We need someone in the cabinet who both enjoys the confidence of the People's Party, but who is also willing to work constructively on Switzerland's future", she said.
Beerli told swissinfo that a break with Swiss political tradition was out of the question. "Throwing the People's Party out and into opposition wouldn't be intelligent. It must remain integrated into the responsibility to govern."
If the main political parties are only prepared to accept a moderate member of the People's Party, then the list is short.
There are two candidates who might be suitable. One is Eveline Widmer-Schlumpf, daughter of Leon Schlumpf, a cabinet member in the 1980s, and herself a member of the cantonal government in Chur. The other is Christoffel Brändli, a member of Senate.
Both have said in the past that they belong "neither to the Blocher nor to the Ogi camp" - a position which could endear them to members of other parties.
by Markus Haefliger