It would help if you cited the actual URL:
In order to "fix" Social Security, the cost rate line must be less than or equal to the income rate line on the first graph. And, it must occur before the trust fund ratio line hits 0% on the second graph.
As you can see, the proposal you cited only puts off the inevitable for about 2 years. Go ahead and look at the others, and try to find one where the trust fund ratio doesn't drop to zero and isn't declining in 2090. The only one I found is the eventual 50% tax increase.
Most massive tax increases are assuming benefit cuts are only applied for newly eligible people.
No, the individual scenarios are run separately. But, you can look at them and get an idea of how much each one actually help. However, I'll caution that you can't just add up the effects -- the SSA explicitly warns against it: Understanding Interaction among Individual Provisions that Would Change the Social Security Program.
A ~50% FICA tax hike won’t fly politically. Existing recipients probably will have to take a benefit cut of at least 6%, at no more than 1% a year.
I didn't say it would fly. I said that's what would be necessary, without a benefit cut. And, 1% a year, even indefinitely, barely makes a dent:
Starting December 2015, reduce the annual COLA by 1 percentage point.
Public pension recipients might be taxed to help out Social Security too.
Public pension recipients are already taxed. My wife pays federal income tax. There's no payroll tax on pension benefits, because it isn't payroll. Her pension contribution was exactly the same percentage as the FICA contribution would have been if she had been contributing to Social Security.