Clinton was the last President to balance the budget. It's been worse since mostly because of failed Republican policies related to deregulation of financial systems.
Presidents don't balance the federal budget. Congress does that.
The last time the budget was balanced was when there was a Republican lead House and Senate. Newt Gingrich lead the House with their Contract with American, and their highest priority was a balanced budget.
That was the year Congress refused to pass the budget until it was balanced. It took until Feb, 5 months after the start of the Fiscal Year, for the budget to be passed. 5 months, or almost half the year, was limited to 80% of the previous year's spending level, which meant there was an extra 20% x 5 months to spend in the remaining 7 months if you consider what was spent the previous FY.
Also, there was a "peace dividend" caused by the end of the Cold War. The active duty ranks were reduced to much smaller numbers while manning was converted to contractors and reservists.
Another thing that helped was the Dot-Com bubble that lasted until 2000 -- the end of Clinton's term. Tax revenues exploded due to a crazy volume of stock trading, in particular day trading.
Many other factors helped, including the tax rate increases passed by Dems controlling Congress during the Reagan and Bush terms.
Bill Clinton had next to nothing to do with the balanced budget other than signing into law what Congress worked out.