That didn't happen until after the Republicans took over the House, in 1994, then Clinton was forced to accept Welfare reforms, and for the first few years, the Republicans toed the line on spending, which created the surplus. The 2001 budget was actually the last budget under the Clinton administration.
Sadly, their majority went to their heads, and Republicans got the earmark fever. That started their upward climb in spending, which only got worse after 9/11, and the downturn in the economy, which lowered revenues, but spending didn't go down to match the decreased revenues. Their profligacy was a major reason the Repubs. lost their majority in Congress. Scared by the election results in 2004, the Repubs slowed spending somewhat, and in 2005 and 2006, the deficits started going down, but when the Dems took over Congress, spending rose dramatically, so there is CLEARLY a difference between the parties!