He is understood to believe he will still win a leadership contest under Labour's primary-style system because of support among members and unions.
However, after talking to colleagues he is weighing up whether his difficulties with the caucus are too entrenched to heal, and what effect that could have on Labour's chances of winning the 2017 election.
Several of Mr Cunliffe's supporters, both MPs and in the wider party, have told the Herald they do not believe it is tenable for him to remain in the role because of pushback from the caucus, and he is being advised to hand over to a new team.
However, the early push by supporters of Mr Robertson to get him installed as leader uncontested could backfire by getting Mr Cunliffe's back up. Mr Robertson tailed Mr Cunliffe significantly in support from party members and unions in last year's contest, and for some in caucus there remain concerns about whether he would have a wide appeal for voters.
Other potential candidates, including Andrew Little and David Shearer, are yet to decide on their positions. Mr Nash and Mr Shearer have both been outspoken about the need to move the party to the centre.
Mr Nash said last night that he had just returned to Parliament and needed to concentrate on consolidating his hold on the Napier seat. Asked about the "One Robertson" solution, he said he was "agnostic" about whether there was a contest. "If there are two or more people who want to be leader there should be; if there is only one person and nobody else feels they can or want to be leader, I'm happy with that."
A source close to Mr Nash said he had come under pressure from the Robertson camp not to stand but his own confidants had also told him he could afford to wait.
Mr Nash did not deny Robertson supporters had spoken to him, but said it had been his own decision.
Mr Robertson has stayed quiet this week but supporters have argued that having only him in the contest would spare the party another costly and potentially divisive run-off under the new leadership rules giving the members and unions a vote.
However, there was also concern it could leave members feeling cheated of their chance to have a say on the leadership and lead to a perception that Mr Robertson did not have a proper mandate.
The party had boasted about its new democratic method of electing the leader. For caucus to abandon it after just one leadership selection could cause a backlash.
Labour got a jump in the polls during the last leadership run-off and renewed interest in the party, including a spike in memberships. Some believe that could be replicated if the timing was right.
