Michael Bachner noticed that he was suddenly hearing from a lot of wealthy callers with bank accounts in Switzerland or the Cayman Islands. They all had the same question: Should they take up the Internal Revenue Service’s new offer of leniency for offshore tax evaders who come clean in the next six months? Or should they risk the crackdown they might face if they don’t take up the offer? “These types of individuals in my experience … they have been engaging in these activities for a long time. They get lawyered up, and they think, ‘What are my chances of getting caught?’ ” says Mr. Bachner, a former Manhattan assistant district attorney who has traveled to Switzerland twice in recent weeks to help clients reach a settlement with the IRS. The IRS could haul in approximately $5 billion to $10 billion this time, says Alex Raskolnikov, a federal tax expert at Columbia Law School in New York. That would be twice as large as the last big federal settlement, a bond-and-options pricing strategy called “Son of Boss” that netted around $3.5 billion in 2004. But it’s still only a fraction of total offshore tax evasion.