Campaigners who are gearing up for the May 18th plebiscite warned that the price tag could balloon to 10 billion francs ($11.3 billion).
"As with all fighter plane deals, on top of the actual purchase price of 3.1 billion francs, you have to add operating and maintenance costs, as well as upgrades needed in the future," Green Party lawmaker Daniel Vischer, a member of the campaign coalition, said in a statement.
Polls show that two-thirds of voters oppose the deal.
Approved by the government in 2011 and backed by parliament last September, it cannot be blocked as such.
But under Swiss law, opponents can contest the legislation that allowed the purchase to be funded by tapping an annual 300 million francs from the neutral country's military budget over 10 years.
The anti-deal coalition is steered by the left-leaning Socialists and Greens, plus anti-militarists who last year lost in a referendum in which voters bucked a European trend and kept their conscript army.
The Gripen's adversaries also include economic liberals opposed to the price.
Referendums form the cornerstone of Switzerland's system of direct democracy, and the campaigners forced a plebiscite by mustering more than 65,000 signatures from voters.
Switzerland picked Swedish group Saab's Gripens over the Rafale jet made by French group Dassault and the Eurofighter of pan-European player EADS.
Supporters of the deal underline that in exchange for the sale, Saab and its engine supplier are contractually bound to sign business deals with Swiss firms worth 2.5 billion francs over the next decade.
The Gripens are meant to replace Switzerland's three-decade old fleet of 54 F-5 Tigers, built by US group Northrop.
The Swiss air force also has 32 F/A 18 Super Hornets built by US company McDonnell Douglas, purchased in 1996.
The military notes that with a combined fleet of 54 Gripens and Super Hornets, Switzerland's fleet would lag far behind the 300 jets in service in the early 1990s.
On Sunday, Swiss media reports highlighted concerns over Saab's decision to fit an American made communication system in the Gripens instead of a planned Swiss-built one, allegedly opening the way for US snooping on data from reconnaissance flights.