There's really only one way to respond to the idea of cutting benefits through formula tweaks:
The premise of the switch from regular CPI to chained CPI is that regular CPI is "too high" relative to the actual level of inflation. But even if that makes the benefit increases "more accurate", you'd only need to do that if you believe the initial benefit is "too high". Which you might believe if you're a DC print or television journalist with a defined benefit pension or 401k, or career civil service employee with a pension, or a political appointee doing a brief tour before selling out to the private sector. But in the real world, a huge number of retirees depend almost entirely on their Social Security checks. There's no good reason that this particular constituency ought to bear the brunt of any budget deal.