It’s worse if you include 401k payments to offset a more generous public pension.
Or really any public pension. I feel like if you're <40 then you should be planning for Social Security to not exist when you get old, anything else seems overly optimistic.
In a few years, given no changes, the cash flow will go negative and we'll begin spending down the trust fund. By 2035 or so (I forget the numbers, and the projections tend to vary widely anyway because of differing models and, yeah, partisan spin) the trust fund will be spent and the social security administration will need to adjust, as it will be taking in something like 80% of obligations.
A 20% shortfall is a big accounting problem. It's hardly "plan for it not to exist".