CSU members of parliament Hans-Peter Uhl and Norbert Geis, as well as state parliamentary representative Christa Matschl all told the Bild newspaper on Saturday that they believed their party, as a member of the ruling coalition, was entitled to the vice-chancellor job, currently held by Free Democratic Party leader Guido Westerwelle.
"Karl-Theodor zu Guttenberg would be an excellent figure for this office, and would convincingly embody the national ambitions of the CSU," Uhl said.
But in the Sunday edition of Bild CSU leader Horst Seehofer denied the suggestion that the popular defence minister's promotion was up for consideration. "The new government is not even three months old," he said. "For that reason alone this discussion is a chimera."
"People don't want a debate about different posts, they want us to do our jobs," he added.
The head of the CSU's national committee Hans-Peter Friedrich also played down the idea that the Bavarian party was dissatisfied with its position in government. "Our three ministers play an important part in government and we have an excellent platform from which to articulate our views," he told the Süddeutsche Zeitung newspaper.
But CSU General Secretary Alexander Dobrindt could not resist a dig at other parties in government: "We like to leave titles without substance to other coalition partners."
Friedrich was similarly not averse to criticising the CSU's allies. He called on Chancellor Angela Merkel to show more leadership: "She must follow a more decisive course," he said. "In central issues she needs to define her position more clearly."
Friedrich accused the chancellor of behaving as if she was still governing a grand coalition with the Social Democratic Party. "Every day without a conflict with the SPD was a good day for her then," he said.
Economy Minister Rainer Brüderle of the government's other coalition party, the Free Democrats, meanwhile called on his colleagues to stop bickering. "It's better for the listener if everyone is singing the same tune," he told the Tagesspiegel newspaper.