This is a common talking point, but it was balanced while Republicans had control of the House and Senate.
http://stats.areppim.com/ressources/usxbudget_1789x2019_572x...
There was a sharp rise in income around 1994, and at the same time spending flattened (due to lower unemployment/lower safety net costs). The two met in 97, then fell off sharply in 2000.
This exactly mirrors the "Dot-com bubble" period start, middle, and end:
https://en.wikipedia.org/wiki/Dot-com_bubble
So neither Bill Clinton or the Republicans can really claim credit. This just happened to be a strong period of economic activity that happened to also drive down costs.