Timothy Egan understated the extent to which the Ryan plan would raise costs for Medicare beneficiaries. He reports that it would double the amount that the typical beneficiary would have to pay for their care. Actually, the Congressional Budget Office projects that it would triple the cost for retirees by 2030, with the ratio rising even higher in later years. (This doesn't take account of the increase in the eligibility age to 67.)
It's worth noting that the vast majority of this additional cost is due to increased payments to the insurance industry and health care industry. The CBO projections imply that only about one-fifth of the increased cost to beneficiaries will be savings to the government.