Rumours that his deputy, Bill English, may be planning to oust him, have been doing the rounds in Wellington in recent days.
But both John Key and Bill English say there is no plot, and that claims of a potential challenge are incorrect.
Signs of a crack in National's usually watertight facade became evident late last year, with Simon Power's decision to leave Parliament to work for Westpac's Private Bank.
Power's time as minister in a National government made him the ideal candidate to head the team at Westpac helping high net worth individuals increase their wealth.
But some people have claimed Power's decision to depart was the result of frustration at John Key's ineffectual leadership.
One party insider, who may or may not actually exist, said Key's popularity was steadily declining, and that National faced the prospect within the next ten years of Key not being regarded by voters as the best person to lead the country.
"He needs to step up and make more of an impact," the insider said or did not say.
Mr Key's leadership has also been under constant attack by political bloggers. They have claimed that Key lacks any vision for the country, is bereft of ideas, and has no interest in helping struggling families.
While most of these political bloggers are left-leaning and therefore naturally hostile to National, the fact that people are saying bad things about a prominent political figure has political journalists excited, particularly since the alternative to political journalists reporting what political bloggers have been writing about a politician, and then having the same political bloggers quoting with approval on their blogs what those political journalists wrote about those same political bloggers, is for those political journalists to do some hard work and write stories about government policies and their impacts on people.
This ongoing criticism of John Key has led to speculation that his deputy, the openly heterosexual Bill English, may be planning a leadership bid in the near future.
In addition to Mr English, most of John Key's close advisers and political staff are understood to be heterosexual. This points to the increasing influence of English at the top of the party and suggests a challenge may be imminent.
Key has denied there is a split, and has said there is no possibility of a challenge.
"Why are you questioning my leadership? Why don't you go pick on David Shearer?" he told reporters. "Why does he get such an easy ride all the time?"