Membership of the Labour Party has soared since the general election and Mr Corbyn believes most of these new members are his supporters.
The hope of his opponents is that many may have become disillusioned with his leadership.
But having spent a day in Leeds meeting new and older members of the local party, I found scant evidence for this.
If anything, Mr Corbyn's supporters seem ever more determined to defend him.
So who are these new members; the so called "Corbynistas"?
I spent time with four of them: Jane Ingham , 65, a retired head teacher, Ged Colgan, 26, a hotel worker, Marvina Newton, 30, a local charity manager and Jane Aitchison, who is in her 40s and is a trade unionist.
What quickly became clear was that, not only was Jeremy Corbyn the main reason they joined the Labour Party, but they remain fiercely loyal to him.
Mr Corbyn, they believe, offers inspiration and change.  In the past Labour had become too similar to the Conservatives; particularly over austerity, they say.
Jeremy Corbyn represented a break with the traditional way of doing politics
"He's unlike anyone," says Marvina. "To me that's what is great about him. He speaks from the heart. "
What was also clear was the disdain all four had for those Labour MPs seemingly determined to oppose Jeremy Corbyn.
"Unfortunately they have been part of a style of politics that has not only failed to win elections but they have been consistently wrong about a whole range of issues," says Ged.
Jane the retired head teacher is similarly unimpressed.
"I'm quite disappointed with the MPs. Do too many of them have too many privileges and just enjoy the privilege of being members of Parliament?"
And there's no disguising the fact these new members are prepared for a fight should Labour MPs continue to refuse to back Mr Corbyn, if he wins this leadership contest.
No-one mentions the D-word, deselection. But the warning signs are clear.
"It's perfectly legitimate for local members to choose who they want to be their candidate at the next election," warns Ged. "I don't see why being an MP should be treated like a job for life."
Jane, the trade unionist, agrees.
"They (the MPs) do feel threatened. We represent change and Jeremy represents huge change and that threatens their very cosy position."
So what of longer-serving party members? How do they view this influx of pro-Corbyn new members ?
Away from the city centre in one of Leeds' more deprived areas, Seacroft, a rock-solid Labour area, I met up with two long-standing party members: Les Wrigglesworth, a former miner, and Melvyn Burton.
They both praise the energy and enthusiasm of the new recruits.
However they are more cautious over how committed these new members will remain to the Labour Party.
Les says they may prove "fair weather" members.
They are both dismissive, however, of claims that many of the new members are so-called "entryists" from Trotskyite and other hard-left groups.
Les dismisses the idea as a "red herring". There may be a few entryists, he says, but only a tiny minority.
Melvyn believes the new members may be "naive" in their views but they are not Trotskyists.
It's only a snap shot but my impression is that even those party members who are not supporters of Jeremy Corbyn are far from happy about the challenge to his leadership.
Some regard it as a distraction from the business of opposing the Conservatives; others as undemocratic; others still as a precursor to a possible all-out civil war or even split in the party.
The difficulty is that Mr Corbyn has become the sticking point.
Many Labour MPs believe he threatens Labour's very survival as a credible political party.
But if they are hoping the membership is poised to turn against him - I found precious little sign of it in Leeds.
There's no disguising the confidence in Jeremy Corbyn's camp about this leadership election.