On the surface it appears remarkable that in both Ireland and Denmark groups representing less than 3 per cent of the Dail and a sixth of the Folketing should be able to muster a sizeable vote when it comes to a referendum.
But today the Danes vote in a referendum on the Amsterdam Treaty and, despite the latest poll evidence that the Yes campaign is some 10 per cent ahead, all here are predicting a nail-biting finish late tonight. The leader of the Yes campaign, Mr Lars Nielsen, warns that his campaign is "bleeding support".
And talk is turning to "what if a No?" with the opposition parties beginning to show that the uneasy No alliance of hard and soft left, Greens, a sprinkling of social democrats and conservatives and the hard right, will fall apart at the seams as each comes up with a different wish list for renegotiating the treaty.
But the reality in the two countries is really very different: Ireland is largely Europhile with Eurosceptic tendencies, while Denmark is basically Eurosceptic but learning slowly to live with the EU.
That fundamental difference is reflected sharply in every Danish party. This country is run by a minority Social-Democrat/Radicals alliance, between a third and a fifth of whose voters oppose the Amsterdam Treaty and whose rank-and-file is deeply divided. The main centrist opposition party, Venstre, has a solid pro-European majority among its voters but the left-wing Socialist People's Party (SPP), akin to Democratic Left, has a majority in its parliamentary grouping in favour of the treaty with two-thirds of its electorate opposed.
In the event of a No, the SPP is likely to pitch for Denmark negotiating with its European partners a complete Danish opt-out from the Schengen passport-free travel area along the lines of that provided for Ireland and Britain. Such an option, short of reopening the treaty negotiations in full may be acceptable to other countries.
The June Movement says that is not enough. Schengen is not just bad for Denmark, its spokesman Mr Lars Kaaber argues, but bad for Europe. It will mean border checkpoints, he says, in the acceding countries, between Poland and the Ukraine, Estonia and Latvia, the Czech Republic and Slovakia, dividing families and businesses.
And he insists that the EU must explicitly set a limit to the march of integration by defining areas of activity that will be off-limits. The treaty negotiations must be reopened.
Such demands are likely to be completely unacceptable to Denmark's fellow member-states with the result that the June Movement and the hard-left People's Movement are certain to remain adamantly opposed to any amended treaty. That raises the embarrassing prospect of the government needing to do a deal with the far-right Danish People's Party and its charismatic leader, Ms Pia Kjaersgaard, who may be able to bring her supporters with her for a second referendum, but at a price.
Her spokesman, Mr Soren Espersen, was confident yesterday a deal could be done. Countries like Germany, Sweden and Britain would not dare force the Danes out of the Union or into a second-class form of membership just to get the treaty ratified, he said, for fear of the popular reaction at home.