Totally false. It was balanced in the 90s. Its just that raising taxes has to be part of the equation. Guess what, three successive republican administrations have lowered taxes. So maybe just roll those back.
For example in the year 2000, people aged over 65 were 12.4% of the U.S. population. Today, that demographic has grown dramatically to 19% of the population. That's fewer people working and paying taxes while also simultaneously drawing more from medicare and social security.
This doesn't mean it's "impossible". But to balance the budget today without major spending cuts would require raising taxes 39%. It's just so different than it was then to make the math work out.
That gives a lot more time to phase in any longer term changes to those programs.