A further 26 percent want no deal at all, according to the representative survey run by the country’s Tamedia group in mid-May.

Meanwhile, 41 percent of voters would prefer to see the Swiss government go back to the negotiating table and win a better deal for Switzerland.

Read also: What you need to know about the draft Swiss–EU deal

Of the group who support new talks, 32 percent said Switzerland’s top priority should be fine tuning the agreement to ensure Swiss wages are better protected against competition from cheaper workers from EU countries.

And 27 percent believe the focus of any new talks should be on getting a guarantee from the EU that Switzerland will not have adopt the EU’s Citizen’s Rights Directive – a move that would most likely lead to higher welfare payments for Swiss-based EU citizens.

The draft Swiss–EU deal (here in French) has been on the table since last November and is the result of years of negotiations designed to update and streamline relations between Bern and Brussels.  These relations are currently based on around 20 main agreements and 100 secondary agreements.

Read also: Swiss government unveils new measures favouring Switzerland-based workers

For Switzerland, keeping Brussels on side is crucial to ensure it continues to have access to the all-important EU Common Market.

The EU has repeatedly stated that the draft deal is non-negotiable and has threatened sanctions – including barring Switzerland’s stock exchange from trading EU company shares – if Switzerland doesn’t sign on by the end of June.

But the Swiss government has so far stood firm in the face of EU pressure to get the deal done and dusted, arguing it needs more time to consult internally given a domestic context of extreme scepticism in the face of all things EU.

Hopes in Brussels that Switzerland might soon sign the deal were dealt a blow on Sunday when Economy Minister Guy Parmelin said new talks were necessary.

“We have listened to all the important players: business, unions, parties, cantons and experts. The government knows there is no majority support for the text as it currently reads,” he told Swiss newspaper SonntagsBlick.

According to the SonntagsZeitung newspaper, current discussions within the Swiss government are not about whether new talks should go ahead, but about when and how.

Read also: Switzerland votes to tighten gun laws, safeguard EU relations