Speculation abounds about Julia Gillard's tenure as prime minister with her personal standing and that of the government slumping in recent opinion polls.
The polls also show voters would prefer Mr Rudd to lead Labor, with one suggesting he could turn around the government's fortunes in Queensland.
Senator Joyce called on Mr Rudd to be straight with the electorate, saying the former prime minister was being self indulgent by obviously campaigning for the leadership.
"If he was fair dinkum, have the ticker, stand up and say this is ridiculous and get this show back under control," he told reporters in Canberra on Monday.
"If he is not just doing that, it is just some fit of pique where he is sulkily going around, trying to throw mud on everybody."
Senator Joyce said if Labor changed leaders, it should choose a new treasurer as well.
"If you are going to change the sheets, change both of them," he said.
Fellow Nationals senator John Williams said Mr Rudd was playing games.
"What he is doing is saying here I am, you knifed me, you sacked me, if you want me to come back, I am not going to do it for you," he told reporters.
Opposition Senate leader Eric Abetz said Ms Gillard had been unable to fix policies on which Mr Rudd had stumbled, citing the mining and carbon taxes, border protection, and returning the budget to surplus.
"Julia Gillard has not been able to make a silk purse out of those sows' ears," he said.