Between floors it came to a halt, and for 20 sticky minutes, Japan's finest economists and deal-makers stood shoulder to shoulder making nervous small talk with their glowering minister. The incident received little coverage in the West, but in Japan it suggested a valuable lesson. For this was no ordinary hotel lift. As the Kyodo news agency pointed out: "The elevator was of US manufacture."
Luckily, the Japanese and Americans were in Canada to talk about US cars not lifts, but the incident symbolised the issues which have clogged their talks over the last 20 months. Throughout the 21,000 man-hours of talks, the US has been repeating three principal demands: more Japanese dealerships in foreign cars, greater US access to the domestic replacement parts market and increased purchases by Japanese manufacturers of US auto-parts.
Exasperated by Japan's failure to come up with any specific goals, Mr Kantor insisted that Japanese manufacturers spell out targets for increased purchases of foreign parts. The targets would be "voluntary", he insisted. But when Mr Hashimoto failed to volunteer them, the talks stopped, a complaint was lodged with the World Trade Organisation and sanctions were promised. They are likely to be published in detail in the next few days.
On their own terms, the Americans have a watertight case. Japan's trade surplus with America is $65.9bn (£41bn), 56 per cent of which is accounted for by vehicles and auto parts. "Over the last 25 years, Japan has sold over 40 million cars to the US, while we sold only 400,000 cars to Japan," a senior US official said in Tokyo last week. "Our market is the largest open market in the world, and it's been indispensable to the growth of the Japanese economy. Japan's market is the largest closed market in the world: it needs to be opened up. These are not opinions, they are facts. Somebody is right, and somebody is wrong."
But several things about this tough approach grate on the Japanese. For a start there is the inherent contradiction in demanding managed export quotas to bring about "free" trade. Then there is the timing of the demands which could hardly come at a worse moment. Japanese exporters in all sectors have been struck hard by the surging yen.
Analysts calculate that the 11 Japanese vehicle makers have the combined capacity to build 14 million cars and trucks a year, around 4 million more than global markets can sustain. Since the bursting of the bubble, painful measures have been taken to improve efficiency and streamline production - but any profits have been swept away by the yen's rise. Toyota recently hinted that it may have to lay off workers, a traumatic step in a country dedicated to lifetime employment.
Above all, Japan refuses to accept the US's right-and-wrong analysis. In theory, the government accepts that it does not import enough and the need for reform. In the 1993 Economic Framework agreement, the two agreed to "a significant expansion of purchases of foreign parts by Japanese firms". There are plenty of reasons for believing that this is taking place.
Quite apart from the slowing down of Japanese exports, total car imports increased by 10 per cent last month against the previous April. The increase for 1993 was 50 per cent. The US points out that, although the percentages have risen, the actual figures are still small. But sceptics cite another reason for Kantor's relentlessness: the fact that, although Japanese consumers are buying more foreign cars, they are less inclined than ever to buy American. British car sales to Japan rose 15 per cent in April to 2,186 units.
But US sales rose by only 4.7 per cent to 7,165, and among the Big Three American auto-makers, the loudest critics of Japan, only Ford's figures were up.
The Americans insist that free trade is their goal, not simply a bigger market share for US companies. "If it's free and open, we're prepared to lose," insisted an official last week. But the European sales figures suggest the problem lies not with Japan's unwillingness to admit foreign competition so much as in America's failure to make cars Japanese consumers want. The vehicles most popular here are saloons. Japan, like Britain, drives on the left but the Big Three offer no right-hand drive model in that saloon category.
To many in Tokyo, the US position is pure arrogance, based on the assumption that, if the Big Three can't make it in Japan, then the markets must by definition be closed.
The European Union, and its Commissioner Leon Britton, have been conspicuous by their failure to offer any explicit support to the US: European carmakers, after all, have a bigger share of Japan's market than they do of America's - 4.9 per cent as opposed to 3.2 per cent.
Since the post-war American Occupation, the US share of Japan's imports has shrunk, as that of Europe and Asia has increased. America's traditional importance as Japan's global "big brother" has dwindled in the post-Cold War vacuum.
America no longer seems to offer the ingredients valued above all by Japanese consumers: quality and after-service.
For that, they turn to their own brands - and if the rest of the world is buying Japanese, why shouldn't the Japanese?
Justly or not, US cars are seen as uneconomical and unreliable. Just like American lifts.