If the republicans were half as fiscally responsible as they claim to be, they would have done it. Hell, Clinton used his economic surplus to pay down the national debt instead of passing out free candy. Republicans haven't been fiscally responsible in decades, and this is something their voters will realize yet again very soon.
The national debt increased every year under Clinton. Despite running surpluses (and the surpluses could also be vewed as an accounting trick if you really want to nit-pick), the debt never went down.
http://www.treasurydirect.gov/govt/reports/pd/histdebt/histdebt_histo4.htm
09/30/1999 5,656,270,901,615.43
09/30/1998 5,526,193,008,897.62
09/30/1997 5,413,146,011,397.34
09/30/1996 5,224,810,939,135.73
09/29/1995 4,973,982,900,709.39
09/30/1994 4,692,749,910,013.32
09/30/1993 4,411,488,883,139.38
09/30/1992 4,064,620,655,521.66
Lets also not forget he had a Republican congress that drastically curtailed his spending plans and forced a lot of reform in regards to the deficit.
And as for being fiscally responsible, I don't think either side can lay claim to that title considering the last 40 years or so.