the moment around six weeks ago when the No campaign had a sudden shiver of panic that it was losing. The polls had been moving in favour of Yes, Better Together's negative messages weren't swaying voters, Labour wasn't doing enough to stir its base, and money was running low.
It all led, says the Scottish LibDem leader, to the "cold realisation we needed to change".
Talking candidly to the Sunday Herald, Rennie says he and his fellow unionists always knew - in theory - that the Yes side could win, given the SNP's Holyrood triumph in 2011, however "we all felt deep down it was only a small possibility"; not any more.
"Six weeks ago there was a wobble," he says. Besides the polls, there were problems with "resources, message discipline and striking the right balance between positive and negative".
Better Together's own supporters noticed too. At public meetings, nervous unionists would ask about the state of the campaign, he admits.
But the episode also "focused minds", and he says Better Together is now better staffed, better financed, and has more confidence and more positive messages.
"I'm calmer now than I was six weeks ago," he says.
He's also effusive about Labour's new input. He can't heap enough praise on Frank Roy, the Motherwell & Wishaw MP who is one of Labour's most effective backroom fixers and is now in the heart of the Better Together operation.
Former PM Gordon Brown has been "outstanding", he says, and he's glad of support from Brown's long-term ally, the Cowdenbeath MSP Alex Rowley.
An ex-MP for Dunfermline and now a list MSP for Mid-Scotland and Fife, Rennie says that in his old stomping ground of Rosyth, one recent estimate had support for Yes at 60-40, despite the No camp's warning over dockyard job losses.
"There is still a huge job to be done in those [Labour] communities. It's partly that feeling about getting rid of the Tories."
With the LibDems and Tories in Coalition, his party seems to be leaving the fight to Labour. The LibDems are majoring in canvassing and leaflet delivery, vital work but low-key.
Those out on the stump, such as MPs Alan Reid, Malcolm Bruce and Michael Moore, and the peers Shirley Williams and David Steel, are working "friendly" areas in the Borders and Highlands.
Rennie is chapping doors in Fife, but with Rowley for company, or possibly bodyguard.
As well as a "revived" Better Together HQ, Rennie says the No side is being helped by voter caution, a too-good-to-be-true Yes campaign that won't admit any frailty, Alex Salmond, and the cross-party offer of more powers.
"I think at the end of the day, if people don't know they'll be naturally cautious," he says.
"I understand desire for change. I'm a liberal. I'm a progressive. I want things to change. But I don't want to grab the first change that comes along just because it sounds good.
"If you don't know, then you vote No."
There's also what he describes as Yes's "fundamental flaw" - refusing to acknowledge downsides to independence.
"People know life's tough and it's not going to change automatically by drawing a line on a map. If you're going to get trust with voters then you have to be frank about what some of the downsides are, and they [the Yes camp] aren't.
"It's 'everything in the UK is bad, apart from the stuff we demand we keep, and everything on our side is great', and it just doesn't wash."
It's a flaw that goes to the top, he says. While Rennie praises John Swinney's probity and Nicola Sturgeon's professionalism, the First Minister is another story.
"It comes from him. Let's just bully and bluster our way through this and say nothing is wrong. Alex Salmond has that reckless nature to him.
"He thinks he's the big asset, but I think he's undermined their campaign in many ways. His ratings are almost as bad as mine now."
According to Ipsos MORI, the FM's approval rating is +5 and Rennie's -20, the lowest of any Scottish leader, but, hey, a LibDem can dream.
Less a dream and more a fantasy, according to the Yes side, is Better Together's offer of further devolution in the event of a No.
Rennie, Ruth Davidson and Johann Lamont posed on Calton Hill last week for a joint declaration on more powers after the 2015 General Election.
The LibDems have the biggest wish list, while Labour and the Tories are focused on income tax.
There is some overlap, but no agreement.
But Rennie insists a shared desire for Holyrood to have more responsibility will ensure a deal.
After tuition fees, he says the LibDems also know "acutely" how voters would punish a U-turn.
"This is rock solid," he says. "The fact we're prepared to step out, no weasel words, straight up, say this is what we're going to do, I think that should convince people.
"I understand people will be sceptical, but they need to know - we definitely mean this."