Earlier this week, the country accepted a demand from the United States to enable Swiss banks to circumvent some elements of secrecy laws and turn over key information to US authorities.
Washington has repeatedly accused Swiss banks of complicity in tax evasion, since they hold billions of dollars belonging to American citizens accused of hiding away taxable income from the US revenue service.
The details of the sum the banks will have to pay US authorities in order to win legal closure is not yet known, but Swiss media have reported that the overall figure could hit ten billion Swiss francs ($10.5 billion).
"The (Swiss) National Bank does not have as a task to save banks when they go insolvent," Thomas Jordan, chairman of the central bank, was quoted as saying in an interview with the Schweiz am Sonntag newspaper.
He said, however, that the bank's mandate is to contribute to the stability of the country's financial system.
A bill on the deal will be put to parliament later this month and the implementation of its provisions will be limited to one year.
With the global economic crisis having put tax havens into sharp focus, Switzerland has fought to defend its long-cherished principle of banking secrecy by giving ground in some areas but declining to allow the automatic handover of account details.
The government said that while the names of US clients can be handed over automatically, their account details can only be disclosed if Washington makes a specific request under rules related to the pursuit of tax dodgers.
Previous reports have said the 300 banks in Switzerland would be ranked by their level of alleged complicity in tax evasion.
The dozen seen as the main offenders would reportedly be forced to make individual deals, while a second category, comprising those with American clients but which have not yet faced legal action in the United States, would have to pay a set fine.
Citing unnamed sources, the NZZ am Sonntag newspaper said the Swiss banks that need to make individual deals will have a time limit of 120 days to do so.
It did not say when the clock would start ticking on such negotiations.