There were no surpluses, there was early tax revenue realization from people rolling their conventional IRAs over into Roth IRAs.
When Roth IRAs started, you could roll your conventional IRA over and take four years to pay the taxes due. The four years of Clinton's "surpluses" were the four years when taxpayers who had rolled their conventional IRAs into Roth IRAs were paying billions in extra taxes.
As soon as the Roth rollover payments were over, the "surpluses" miraculously disappeared.
The press would never have pointed out the obvious. They were desperate to credit Clinton with anything and everything good that they could.
Thats not the whole story, though that may have been a factor. You will see that Capital Gains revenues, Corporate Tax revenues and Dividend income also took a dive post-bubble.