"There are hungry-looking women sitting not far from me," he whispers conspiratorially. "They're almost demanding I stop talking."
Nearby, as the interview wraps up, his fellow Yes campaigners are circling in on a birthday cake and Irn-Bru laid out to mark the organisation's first anniversary.
Since its launch on May 25 last year, Yes Scotland has racked up impressive statistics. Last week, it announced 372,000 people has signed its "Yes Declaration", a good way short of its 1 million target, but a healthy 230,000 more than six months ago.
It has also hosted 1184 events, recruited 2671 "Yes Ambassadors", set up 173 local groups, and distributed 3.2 million leaflets; not to mention attracting more than 17,000 followers on Twitter and more than 56,000 Facebook "likes".
But another set of figures threatens to turn the birthday as flat as day-old champagne: the opinion polls.
In the 10 polls published since January, support for independence has averaged 33% against 51% for the Union, and 16% undecided, a pattern virtually unchanged in a year. The apparent stagnation is used by the Unionist side as a taunt against Yes Scotland and the SNP.
A professional optimist, Jenkins insists the figures don't reflect the settled will of the Scottish people, and will change.
He also says Yes Scotland's internal polling is closer to one survey which reported 36% Yes, 44% No and 20% undecided.
"I think we're where we would have expected to be at this time," he says. "I'm in no doubt that polls will move our way as we move deeper into the campaign.
"What I don't encounter in Scotland is anyone who says, 'I was voting Yes but now I'm voting No'. I just don't hear that at all. The direction of travel is to Yes. There's no doubt about that."
Having been inside the political bubble for years as a BBC Scotland executive, Jenkins has been surprised by the lack of knowledge about the referendum that he has encountered in public meetings.
"It's quite obvious that quite a lot of people are not paying attention, they'll pick it up later in the day. People have busy lives, and people have tuned out of party politics to a large extent. That's why I stress it's much bigger than party politics."
That same lack of engagement makes him think people won't decide how to vote until they are on the cusp of the September 18 ballot next year. He says a key factor is that most Scots already wanted Holyrood to have more powers.
"The job is to convert that view into people voting Yes. There's no doubt people are attracted by the notion of the important decisions being taken in Scotland.
"We are also beginning to row back the myths people have had in the past about the relative strength of Scotland in the UK. The notion that the Scottish economy is actually a strong economy is now something that's taking hold.
"People understand this is an opportunity to shape the direction, the destiny of their country, take charge of our own affairs, make history. I think that will become quite profound next year and will become a major influence."
He is also dismissive of his Better Together rivals, denying they are the slick operation portrayed in the media.
"I don't want to criticise the competence of anyone.. [but] there's nothing they've done that we have found either particularly impressive or surprising."
But Jenkins's contentment is not universally shared within Yes Scotland.
Indeed, two of his own board members – Green MSP Patrick Harvie and Scottish Socialist leader Colin Fox – say the campaign has failed to make the progress expected in 12 months.
"It would be a nonsense to suggest that everything's fine, we're exactly where we want to be," says Fox. "A year ago we would have expected to have been ahead in the polls or at least level pegging. The fact they haven't budged is an issue that requires our ongoing attention.
"I think everyone at the Yes Scotland office will have as their priority movement in the polls. I think they'll be disappointed over the year that the polls haven't moved. But my sense is this is still winnable."
Others in the Radical Independence movement are far harsher.
"They look like cowards," says one of the leading figures on the left, who doesn't want to be named but feels Yes Scotland is failing to generate headlines.
"Anyone can sit at their desk pumping out infographics or playing with social media. But no matter what they say, this is not going to be won on Facebook or Twitter."
The Yes campaign is "certainly behind where I'd want it to be," says Harvie.
"This is a challenging debate to be in. In some ways, the No side only needs to keep people confused. We need to do much more than they need to do."
THE last year has also exposed some of the divisions in Yes Scotland, with the Greens and Socialists aligned against the SNP on the monarchy, currency and Nato membership.
If the differences were no secret before the campaign, they have been exploited by Better Together in its effort to equate independence with uncertainty, as it argues even the Yes side can't agree on what independence would mean.
At the launch of the SNP Government paper on the economic case for independence, Alex Salmond suggested a Yes vote could lead to corporation tax at 3% below the UK rate.
As Chancellor George Osborne is cutting that to 20% by 2015, it would mean a new-minted Scotland asking companies to hand over just 17% of their profits.
It's a "huge mistake", says Harvie given the global backlash against firms such as Apple and Google routing profits through Ireland because of its ultra-low 12.5% rate.
"I think the position the SNP are taking is not sustainable. It's very clear that corporate tax avoidance is one of the main mechanisms by which the gap between rich and poor has continued to increase under Labour, the Tories and the Coalition. Let's not have it happen in Scotland as well. You've even got Republicans in the US talking about cutting down on corporate tax avoidance.
"The whole world, including a lot of these big corporate tax avoiders, are coming to recognise it's time to take their noses out of the trough. Things are going to change now. I think Scotland should be part of that change."
Better Together has its frictions too, however.
The fear and loathing between Labour and the Tories bubbled over at the recent launch of a Labour pro-union vehicle, United with Labour, when Gordon Brown gave a speech that seemed more about bashing the Conservatives that the Nationalists.
But, for now, Yes Scotland is suffering the brunt of the criticism over internal divides, perhaps as a consequence of those awkward polls. If it was in the lead, or even on the up, it could swagger its way through the rows.
Shadow Scottish secretary Margaret Curran says the past year has been one of "confusion and disarray from the SNP".
Michael Moore, the LibDem Scottish Secretary, says the first year of the Yes campaign has been characterised by over-simplistic and unsound assertions from the SNP and attacks on its critics, followed by grudging admissions that independence was not clear cut after all.
"Serious questions are now coming thick and fast. They have to be considered seriously, not ignored or batted aside contemptuously.
"The debate has to be for real."