Now that National has no power to lose, that disincentive has gone.
MPs are looking for someone to blame for ending up in Opposition and the Winston Peters voodoo doll is getting somewhat tattered.
Given that English led the party to a healthy 44.4 per cent result at the election and that he is making a good fist of Leader of the Opposition, Bennett and Joyce are the next best targets.
Despite her public popularity, Bennett is not very popular in the caucus and if she were challenged for the deputy leadership, there is a good chance she would lose.
Joyce has held a powerful position in the National Party ever since he headed its review and restructuring after the 2002 election and has run the last five campaigns for National. What he says goes.
No one ever challenged a finance spokesman but if Joyce, a list MP, were to resign from Parliament to pursue business interests, there would a lot of silent clapping from the caucus.
He lost the Northland byelection to Peters when he wasn't meant to, he won it back when he wasn't meant to, and he ran the campaign that saw National lose power.
English will want to demand more discipline from his caucus but he cannot be blind to the need to manage some rejuvenation, if not a succession.
The speculation of the past day will have been very damaging for National and ultimately destabilising for English.
Discontent within the caucus equals disunity to the public and disunity spells decline to political parties.
Last night's Newshub poll in which National on 44.5 per cent remained near its election high may turn out to be National's high-water mark this term.
And if the party starts heading south, there will be no incentive for English to stay.