Democrats believe the best way to reform Medicare is to leave the program intact but vastly strengthen its ability to pay for quality. Republicans believe the best way to reform Medicare is to fracture the system between private plans and traditional Medicare and let competition do its work.
It’s worth saying there’s no particularly good evidence for either option.
It's worth adding, however, that the profit motive which underlies private plans means that the pools of potential customers would be arranged concentrically, from less healthy and usually older consumers on the outside rings, paying more, to healthier and probably younger consumers on the inside, paying less. The real bodily basket cases are then dispatched to traditional Medicare, which can deny no one, yet Medicare (which would be ratcheting down its payments to providers) would in no way meet actual healthcare costs, thus those consumers would get stuck with the difference--and good luck finding an affordable supplemental plan, as you suffer from heart disease, emphysemia and cancer.
And for all this there is pretty good evidence; that being the entire history of private healthcare.
postscript: I should also add that Klein does go on to note that "Competition hasn’t worked very well in the health-care system." I didn't mean to be unfair to Klein, who's one of the best analysts around, but perhaps I was. My point was simply that the profit motive has no ethical place in a social field as vital as healthcare.