Sure, that was the name — actually, the Patient Protection and Affordable Care Act — assigned to the 2010 federal health care reform law. But as San Francisco Chronicle columnist Debra Saunders reminds us, the claim of affordability clearly falls short of the mark.

As a candidate for president, Barack Obama sold his signature universal health care plan with the promise that it would “cut the cost of a typical family’s premium by up to $2,500 a year.”

Now that the Affordable Care Act exchanges are open for business, voters are finding that the biggest problem with Obamacare is not that some websites crashed last week but that the Obama promise of big savings for the average family was too good to be true.

Now that the exchanges are open for business, people who already have individual coverage have something new not to like: sticker shock. The Affordable Care Act isn’t affordable after all.

Last week, I began hearing from readers whose individual policy premiums are going up, not down. A local architect sent me a notice he received from Kaiser Permanente informing him that his individual coverage will increase by $199.95 per month, or 78.9 percent. When he added his two sons, the percentage increase was even greater.

A freelance journalist told me she made $98,000 last year. But she and her retired husband, both 51, wouldn’t pay $7,200 in premiums for high-deductible coverage. It’s cheaper to pay the fine, she said. Besides, she added, “we’re healthy.”

A reader wrote that her premiums will rise considerably, and she doesn’t think she qualifies for a subsidy.

It is becoming increasingly clear that while poor working families will have access to their own health care policies at affordable rates — affordable because they are subsidized — middle-class and affluent people stand to pay more. Forget that $2,500 savings.

And this observer is less convinced than Saunders about the percentage of “poor working families” that will benefit from the new law. Those subsidies depend on other portions of the law proceeding as promised, a dubious proposition at best.