Health and Human Services Secretary Kathleen Sebelius took a jab at the Republican health care platform, arguing that "What's missing from the Romney-Ryan plan for Medicare is Medicare."

She followed up with the claim that Medicare would cost seniors "$6,400 more" annually.

It's a great rhetorical attack, but there's one big problem: That $6,400 figure comes from an independent analysis of the budget that Rep. Paul Ryan (R-Wisc.) authored in 2011. And that budget looks pretty different from the plan that Gov. Mitt Romney has outlined.

Here's where it gets a bit confusing: Back in 2011, Ryan wrote a budget that would dramatically overhaul Medicare. It would eliminate a publicly-run Medicare plan, and replace that with private plans that would compete for seniors' business.

Multiple think tanks used Congressional Budget Office data to estimate the impact that Ryan budget would have on seniors. And they did indeed find that Medicare beneficiaries would end up spending more.

The Center for Budget Priorities and Policy estimated seniors would eventually pay $6,400 more for their Medicare benefits. The independent Kaiser Family Foundation had a slightly different estimate of $6,870. Politifact has looked through the various estimates and finds they are "all in the same ballpark."

That's where the numbers come from. At the time, Romney said that "anyone who has read my book knows that we" -- meaning him and Ryan -- "are on the same page.” But when Romney outlined his own plan Medicare, it was substantially different. The Republican governor does envision a bigger role for private plans that administer Medicare benefits. But he doesn't eliminate traditional Medicare outright, nor tie his vouchers to the low growth rate that led to the $6,400 estimate. Here's how it's put on the campaign's website:

“Traditional” fee-for-service Medicare will be offered by the government as an insurance plan, meaning that seniors can purchase that form of coverage if they prefer it; however, if it costs the government more to provide that service than it costs private plans to offer their versions, then the premiums charged by the government will have to be higher and seniors will have to pay the difference to enroll in the traditional Medicare option

It's also worth noting that Rep. Ryan's more recent budget would also maintain Medicare as one option among private plans, after his first budget saw significant blow back.

Could traditional Medicare become more expensive than the private plans? That's certainly a possibility -- the Medicare voucher seniors receive could fail to cover the cost of purchasing the public option. And Romney does turn the plan from a defined-benefit to a defined-contribution, which substantially changes Medicare. But it doesn't eliminate traditional Medicare as an option, and the $6,400 figure is an estimate of an entirely different plan.