You would expect him to appear unfazed by the pressure, and you would be right. The Cabinet Secretary for Finance, Employment and Sustainable Growth is his usual measured and courteous self when he meets the Sunday Herald in his medium-sized office in the Scottish Parliament, on a day when he unveiled a new £85,000 package of support to women entrepreneurs.
With less than 200 days of campaigning and governing before referendum polling day, and with business and the economy staying front and centre of the national debate, we invite Swinney to take stock of the central argument over independence. What more does he need to do to convince waverers to vote Yes?
His reply is characteristically understated: "To ensure that the public are equipped with information about the financial strength of an independent Scotland."
The approach he will take is to stress the qualities of independence as a logical add-on to devolution.
"If you look at the economic performance of Scotland since the establishment of the Scottish Parliament, Scotland's economic performance has improved and strengthened with limited decision-making powers," he says.
"Therefore, with a broader range of powers and levers, we can improve that economic performance yet further - that's essentially the core of the argument that we will set out.
"I suppose the two themes of our message are that Scotland has the attributes and the strengths to be an independent economy, but then also that there are opportunities that become available to us in exercising distinctive responsibility. We have maxed out the limited powers we've had, and we want to go further as a consequence of exercising the powers of independence."
Ability to remain unruffled is at a premium in a week when business people and economists, at least some of them disinterested, have queued up to spoil the Yes campaign's smooth continuity narrative.
Swinney can point to a clutch of high-profile business endorsements, including Willie Walsh, the head of International Airlines Group, BA's parent, who the previous week endorsed the Yes campaign's message of "increased opportunities" from a Yes vote.
This week has provided less covering fire, and while the influence of big business on the undecided voter is hard to assess, people at least trust commerce to follow the money. Although the pro-independence left might celebrate unpopularity in this quarter, it is bad for the credibility of the Yes proposition that so far none of Scotland's industries, strategic, iconic, or otherwise, is collectively saying that independence will have them laughing all the way to the bank.
Instead, industry groups and businesses themselves are largely sitting firmly on their hands (Aviva, Federation of Small Business Scotland, Scottish Tourism Alliance, Scottish Food and Drink Federation, Society of Chemical Industry Scotland, information technology group ScotlandIS), or making discouraging noises (Scottish Financial Enterprise, Scottish Chambers of Commerce, the Scotch Whisky Association) or being explicitly, sometimes volubly negative (Alliance Trust, Standard Life, Shell, BP, RBS, Barclays, Lloyds, Aggreko, Weir Group, CBI Scotland).
Swinney looks surprised when asked why no strategic Scottish industry has collectively declared that independence is unequivocally in its members' interests.
He counters by citing Business for Scotland, a cross-sector support organisation made up of long-time true believers and recent pragmatic converts, that makes well-placed interventions and counter-thrusts in the indy propaganda "air war".
"What's important is that do you have business voices that are arguing would it be better for Scotland to be independent country? Yes, we have that, we have a very well-supported, extensive organisation in Business for Scotland who have, the last I had heard, in excess of 1500 members who are actively participating very effectively in the debate to make the arguments for the realisation of the economic opportunities of independence. I think they are fulfilling that role very effectively.
"There is a long way to go in the campaign but I think we have succeeded in setting out a very strong and positive proposition of how Scotland can prosper with independence. The high point for me was the publication of [the White Paper] Scotland's Future in November, which captures all of the arguments in one place about the economic strength of Scotland, the opportunities opened up by independence, and the way in which we can integrate areas of policy like welfare and benefits policy with tax policy and employability policy, to actually tackle some of the fundamental issues of inequality in Scotland.
"These have historically been viewed as social issues but I view them very much as economic issues. Without tackling them, Scotland will continue to underperform economically."
Another big theme of the week was the continued reverberations of the currency issue, with the Scottish Government's Fiscal Commission reaffirming its belief that a new UK-wide monetary union is the only route the Yes campaign need to pursue.
The Scottish Government's main argument leans on an aversion to imposing exchange costs for UK businesses selling to Scotland. Which begs the question of why did this not prevent the SNP from advocating Scotland joining the Eurozone as recently as 2009?
"If you look back at the history of the Euro, various administrations have come to particular views about that. What we have tried to do with this proposition is to show in a practical scenario we will be facing just short of 200 days time, there is a necessity for us to focus on how we construct a currency union, and one of the issues that will be material will be the level of transaction charges if the UK doesn't agree to it. Now, the other issue which will be material is about debt. If you follow the logic of the Chancellor's logic in Edinburgh, the Chancellor is saying that he views the UK as a continuing state and if you follow that logic, the Chancellor is taking £130 billion worth of debt that he really doesn't need to take, because we are happy to take up to that kind of level on negotiation."
Chairman of the Fiscal Commission Working Group on currency, Crawford Beveridge, last week admitted that the Chancellor's reluctance to enter a currency zone was an unpleasant surprise ("We hadn't anticipated that decision would come upon us"). No professional politician, and certainly not John Swinney, would admit to being blindsided.
"Of course I was expecting it. This is a political campaign. Their contribution could have been predicted on the back of any fag packet. [Ruling out a currency zone] is the easiest tool in the box to deploy.
"What is more important is the speech by the governor of the Bank of England. What that was was a dispassionate analysis of the ingredients you would require for a currency union. I read that speech thinking 'thank goodness we commissioned the Fiscal Commission to explore all these details' because there was nothing in the governor's speech about the makeup, the composition, the architecture, the operation of a currency zone that had not been contemplated by the Fiscal Commission to which the [Scottish] Government had already responded and then formulated the proposition. Of course, that was then dealt with politically by George Osborne, Danny Alexander and Ed Balls, but people will be well served to look at the substance of what the governor had to say because that gives a much clearer insight into how a currency zone would actually operate. Much more so, and in a much more informative way than anything the Chancellor might have said on his day trip - morning trip, in fact, it wasn't even a day trip."
With Chief Secretary to the Treasury Danny Alexander underlining the UK's reluctance to embrace a new pan-UK monetary structure, Swinney may hope that the Mark Carney does not undermine the Scottish Government's implication that the bank is effectively endorsement of the Fiscal Commission's thinking on monetary union.
Readers of Carney's speech will note that he had at least as much to say about the downsides of a monetary union, especially for a 10% shareholder, and noted that "the high degree of integration between Scotland and the rest of the UK may, in part, depend on them being part of the same sovereign nation". Meantime, the Scottish Government's most credible fiscal hawk continues to perform a high-wire feat of political positioning that inspires gasps from friend and foe alike.
Swinney must simultaneously maintain that Scotland's near-top ranking performance in the UK is an endorsement of the actions of successive devolved Scottish administrations, but achieved in near-miraculous defiance of an inadequate constitutional framework.
No less complex a sell is the proposition that Scots can put their faith in a spectacular outbreak of cross-border goodwill and constructive engagement in the event of independence, while relentlessly decrying the absence of these qualities and silkily implying non cooperation over debt.
Long-term Swinney watchers will bet that not only can he keep up these acrobatics until September 18, he will make them look effortless and commonsensical.