Let's say that, on the day of your birth, the government deposits $100,000 dollars (the amount is debatable, obviously) into an FDIC-insured account for you. It earns interest -- not whopping, but nice -- and becomes your property (principal and interest), tax free, on your 18th birthday. This money is now yours to do with as you please: stocks, bonds, college, trade school, travel, investment in your own business, down payment on a house, savings, whatever. If you lose your job, it's money to retrain. It can fund a retirement nest egg. It can pay for a battered wife to pick up and leave, or a widow to make a new start. With some wise planning, it can do quite a few of these things over the years.
Here's the catch: This will represent the entirety of federal benefits for your lifetime. In return for this investment, the U.S. government removes itself from the entitlement racket for good.
Secondarily, states, counties, and towns are free provide relief, as they see fit, through that wonderful system called federalism. Want to move to a town that offers unemployment insurance? Your choice, and you'll pay for it in your city or property taxes. Obviously, it's imperfect -- one may not have unbounded choice of where to live -- but it sets up a situation where towns can essentially bid for residents, who then purchase, via taxes, the level of services they want.
There are certainly things that would need ironing out, but I think it's a workable idea. It would certainly save money.