Treasurer Scott Morrison quoted House of Cards when asked by 2GB Radio whether he agreed the former Labor leader wasn't qualified for the job.
"You may well say that Ray, I couldn't possible comment," he said.
Cabinet secretary Arthur Sinodinos spoke against Rudd's nomination, questioning why the government should back him when Labor wouldn't for a full term as prime minister.
"I'm not spilling any secrets to say there would be a lot of people on our side of politics who say they have reservations about supporting Kevin," Sinodinos told ABC's Lateline on Monday.
Former speaker Bronwyn Bishop issued this brutal burn: "if you have got a problem with the United Nations and you really want to see its powers lessened, send Kevin".
Liberal backbencher Cory Bernardi gave a similar decree, saying the only reason to nominate Rudd would be to destroy the UN from within.
"His megalomania, his narcissism, his arrogance and the dysfunction [mean] we should not inflict him on the United Nations," Bernardi said.