I didn't see anything in the Wikipedia article mentioning Clinton other than him signing the bill. But it does mention that the bill was introduced by a Republican senator and as you mentioned, had support from 97% of Congress which is well above the presidential veto threshold. Was this something specifically that Clinton was pushing for at the time that wasn't mentioned in the Wikipedia article? I was too young to be paying attention to politics in 96 so I don't know the historical context.