Obama also cut the deficit by more than half. It didn't get all the way to a balanced budget because of how bad of a mess Bush left to clean up, but it was moving in the right direction.
And as a sibling post noted, Bush senior also both raised taxes and lowered spending on a relative basis. So the original assertion is decisively disproven -- half of our modern era presidents (along with the Congress they presided over) did not behave the way they said "only happens".
Incentives are key. If Congress does not present a balanced budget then there has to be consequences. Many other countries work this way. No balanced budget forthcoming? Then there is an immediate collapse of the current government or ruling party and run-off elections to replace them.
The issue with requiring balanced budgets at the federal level is there are a number of situations where, by any economic theory, you want to run deficits.
So what you really need is an impartial Fed-budgetary-counterpart arbiter that declares when balanced budget rules are and aren't in effect.
And probably toss in what target percent of debt needs to be paid down too.
Contract with America convinced enough rubes in America that Republicans actually had a plan (which netted them Congress!) It was a giant failure in terms of actually accomplishing a fraction of the goals it set out, though.
Does Clinton deserve a. Ok the credit, for signing off on it? No, of course not. He deserves some of the credit. The rest goes to the Republican congress, which did the budgeting.