Though I expect a reaction that is both more level-headed and apathetic, especially from the Danish, since they have lately also been keen on the xenophobia front (re-instated border controls a few years back).
The problem with this is that the Eurocrats see Europe's political integration as a one-way street: once you are in, there is no way back. They hate and threaten anyone who wants to go a step back - even if it is just a small one. The root cause is their fear of others imitating the Swiss and Brussels losing power. This has become very apparent during the euro crisis: while there are lots of rules for joining the euro-zone, none of the treaties ever even mentioned how one could leave it again. Leaving is just not an option in the minds of European politicians. This leaves no room for experiments and makes the EU very inflexible.
And, in this specific case, we can not trash a part of a treat hoping the rest will be still accepted without problems, that is not the way contracts work.
Democracy means that the Swiss are free to make their choices, and bear the consequences, like every other democracy.
In reality, you always have to make compromises. Pure democracy, in which the vox populi is total imperative must lead to isolationism in todays multi-faceted, complicated world. The best IMO best way to deal with todays world is the parlamentary democracy, where the citizens decide on the big questions and choices of direction while the technocrats try to work things out as close as possible to the stated choice of the electorate.
Picking out a tiny fragment of a big international treaty with many interested parties and rejecting that after the fact is childish.
[1] http://en.wikipedia.org/wiki/Switzerland%E2%80%93European_Un...