In their ongoing battle to convince Americans to believe what the Obama administration is peddling to them rather than what their own experiences are indicating to them, the White House sent out yet another tweet yesterday that looks like it was meant to help combat some of the fury over the great myth that was “If you like your plan, you can keep it“:

Thanks to #Obamacare, insurers CAN’T: 1. Deny you coverage. 2. Drop you if you get sick. 3. Drop you as a customer. pic.twitter.com/t4KL1i0sds

— The White House (@WhiteHouse) November 1, 2013

Number three especially appears to be part of the obligatory spin on the issue now: Obama never really promised that you could keep your same insurance plan, but rather that you could keep your same insurer. If you don’t actually want to purchase one of the more expensive, more ‘comprehensive’ plans that your insurer is now offering after they were required to cancel your previous plan, well, that’s your problem.

…And it is a problem, for quite a hefty number of people. The Associated Press reports on the case of the Griffins, a middle-class couple among the millions of people nationwide who buy individual insurance policies and are now receiving notices that those policies are being discontinued:

Dean Griffin liked the health insurance he purchased for himself and his wife three years ago and thought he’d be able to keep the plan even after the federal Affordable Care Act took effect.

But the 64-year-old recently received a letter notifying him the plan was being canceled because it didn’t cover certain benefits required under the law.

The Griffins, who live near Philadelphia, pay $770 monthly for their soon-to-be-terminated health care plan with a $2,500 deductible. The cheapest plan they found on their state insurance exchange was a so-called bronze plan charging a $1,275 monthly premium with deductibles totaling $12,700. It covers only providers in Pennsylvania, so the couple, who live near Delaware, won’t be able to see doctors they’ve used for more than a decade. …

They can buy different policies directly from insurers for 2014 or sign up for plans on state insurance exchanges. While lower-income people could see lower costs because of government subsidies, many in the middle class may get rude awakenings when they access the websites and realize they’ll have to pay significantly more. …

The Griffins, the AP notes, are considering paying the federal penalty rather than buying insurance, because they’re unlikely to run up the almost $13,000 tab it would take for the insurance to kick in — and if more and more of those mere “5 percent of Americans” subject to policy cancellations the administration keeps talking about are thinking this way, ObamaCare is in deep trouble.