Then 1994 happened, and the Contract With America. The Republicans took both the House and the Senate, and they passed a balanced budget , then, whether Clinton liked it or not.
So that's what "Clinton" did. He pretended he was going to do something, and the Republicans called his bluff, and made him do it.
Note well: Republican majorities in any other set of circumstances have not yielded a balanced budget. I'm not saying that they're the answer (what they did under Trump shows that they very clearly are not the answer for fiscal responsibility). All I'm saying is that "Clinton balanced the budget", while technically true, isn't really the way that played out.