He seems to be referring to this Eurobarometer poll on Civil Justice in the EU, carried out in November-December 2007 and published this April. (Though I can't find the exact question that gives this response). However, that larger numbers of people are concerned by these problems than 2% seems clear.
And one can argue, of course, that if things were better organized, there'd be a lot more than 2% of citizens moving around and settling in other countries.
One can also argue that, if we're going to give in to the sovereignists on everything, why then they win, and we all go back to our little national boundaries and see how long it takes us to start up a good war.
Yet, though instrumentalized, (sov-nat-xen) remain marginal. Were these elements to take over, it would be national preference, protectionism, goodbye single market, and that is not in the interests of transnational corporates. (I don't know if it's a valid analogy, but the GOP has greatly benefited from working wedge issues in the culture wars, while it would certainly not wish to be taken over by the Christian Right: use them but sideline them is the strategy). So, in fact, we don't see the nationalist right winning elections in the majority of cases. It's not true that the heads of government that form the European Council are all "petty sovereigntists".
At the same time, it may well be that there is a considerable constituency (well beyond 2%, as supported by the poll, and by the fact that far more than 2% have had at some time some experience of cross-border exchanges and understand the need for better regulation) in favour of a more useful role for the EU in facilitating individual citizens' lives in nitty-gritty, vital aspects. Giving real content to European citizenship is an excellent way of combating the sovereignists because it is highly likely to be popular. And I'm not sure they have the clout to prevent measures of the kind Lamassoure suggests from being passed - if Council and Parliament decide, under the pressure of negative voting in referendums, that they really must do something to bring citizens into the game.