The economics minister, Pascal Couchepin, said on Sunday that the influential right-wing member of the People's Party, Christoph Blocher, would be unhappy in government.
In an interview with the "Sonntagszeitung", Couchepin said Blocher had a different opinion to the government on a range of issues, and would not enjoy having to stand by government policy.
Couchepin's comments follow the announcement by the president and People's Party minister, Adolf Ogi, that he plans to step down in December.
No candidate from the party to replace Ogi has been formally declared, but Couchepin said whoever stood could find themselves in a similar position.
Although in government, the People's Party has frequently criticised policy, and has itself been attacked for failing to stand by Ogi.
Meanwhile, the president of the right-wing People's Party, Ueli Maurer, has said that he wants just one candidate to be put forward to succeed Ogi.
After Ogi announced he was stepping down after 13 years in government, several politicians called for the People's Party to put forward two candidates.
At present, the party is split between the Zurich wing, which represents the more right-wing members of the party, and the Berne wing, which is more moderate. Maurer stated that any successor must represent the dominant party line.
Further, Maurer said the party would feel no obligation to put forward a moderate candidate.
According to Maurer, Ogi's views no longer coincide with those of the party. Ogi's pro-European Union stance now clashes with the party line which is opposed to Swiss EU accession.
Switzerland's governing parties have criticised the People's Party for, they say, acting like a member of the opposition while remaining in government.
swissinfo with agencies