As The Economist notes, this puts the EU in a bind: does it bring these agreements to an end and uphold the single market, or does it try to accommodate Switzerland for fear of inflating the Swiss vote? The Commission is quick to highlight the sanctity of free movement at every opportunity, but it is a delicate situation: the referendum doesn't have immediate effect, as the quota system needs to be drawn up and implemented. So when and how should the EU approach the question of bringing the single market agreements to an end? The EU should not come across as heavy handed - above all the decision of the Swiss electorate must be respected. But the relationship runs in two directions, and the Swiss should not be allowed to benefit from the single market without extending the same rights to the rest of the EU.
In the end, the issue will have to be confronted. Accommodation of the dilution of the single market unpicks the EU and the commitments Member States, and in this case also Switzerland, have made. If Switzerland chooses to opt out, then that's their choice, but it entails opting out of the single market, not just the parts they don't like. The EU should wait for the Swiss proposals, while making clear that they will stick by the treaties with Switzerland.
For Eurosceptics, the Swiss result is a victory, but the real question is if it is accommodated by the EU system. If it is, then the question will be: why not restrict free movement within the EU? It is one thing to say that the free movement rights are key to the single market, it's another to stand up politically for the benefits they bring and for the integrity of the single market as a whole. In the referendum, the impact of the result on Swiss access to the single market was debated. If Switzerland breaches its EU treaties and brings them to an end, that is their decision.