Switzerland has already had experience of car free days.
In 1973, due to a petrol crisis, the government imposed a car ban for several Sundays.
Campaigners for the current car-free proposal claim there were no problems or complaints by the public 30 years ago.
They also point to similar car-free proposals in Switzerland's neighbouring countries which, they say, have been well received.
France, Germany and Italy have all introduced car-free days, although they are limited to certain areas or parts of a city.
In France, the roads along the River Seine in central Paris are regularly closed off to cars during the summer.
Some of Italy's main cities also impose car bans in winter because of too much pollution. In Bologna, the entire city centre has been closed off.
If the car-free Sunday campaign doesn't succeed in attracting voters, campaigners say they would consider scaling down their proposal to a ban on cars in certain cities, modelled on their European neighbours.
swissinfo, Joanne Shields