The current round of negotiations were directly triggered by Switzerland trying to restrict freedom of movement and realizing they couldn't do that without cancelling all the treaties.

The EU can afford to stick to its guns in this indefinitely. It's made it clear for a decade that any change to the treaties with Switzerland can contain minor concessions, but only in return for a bet reduction in the deviations from the EEA framework.

With respect to euro scepticism, that largely fell apart thanks to Brexit - most of the parties arguing for the same for their countries have moderated their stances significantly, and support for the EU increased massively. Including in the UK where Brexit is widely seen as a massive mistake, and it's more a question of electoral calculus (neither of the big parties can afford to alienate the Brexit diehards yet; they're spread across the political labdscape) than anything else when rejoining gets in the political agenda.