With a Democrat-controlled Congress, any program to balancing the budget would involve taxing one's way to fiscal responsibility, vice reining in Federal spending. It was akin to telling a lard-butt, "We are going to reduce your weight by doubling your caloric intake and buying you larger pants." Democrats talked a lot of smack about fiscal responsibility, but consistently refused to actually do it by reducing (or even slowing the growth) of Federal program budgets.
The CBO budget projections in November 1994 (the Democrats' own projections) were that the Federal deficit would remain around $200B except 1996 (Presidential election year) when they would dip to $120, then back up to $200B for the rest of the decade.
The Republicans ran on the Contract with America in 1994 (including a Fiscal Responsibility Act, and a line-item veto), and won big.
Over the balance of the Decade, the Republican-controlled Congress fought Bill Clinton tooth and nail and dragged Clinton kicking and screaming to a balanced budget in FY 2000. The Clinton Administration fought against the line-item veto in court and the court, somehow found it unconstitutional.
The Republicans balanced the budget by killing stupid unconstitutional budget line items, and slowing the growth of others, which is the only way to balance the budget. You have to starve The Beast.
Democrats talked smack in 1993. Republicans delivered in FY 2000.