If one looks just at the raw, bottom-line number the Department of Health and Human Services released Wednesday—365,000 citizens enrolled since October 1—one might be inclined to think it’s not so hot. And it isn’t. That’s 180,000 or so a month, and if you post that number against the stated goal of 7 million by next spring, the stated goal looks awfully chimerical, and the thing seems a disaster (180,000 times six months, the enrollment period, is just 1.08 million).

Dig a little deeper and things look considerably better. If we could graph it, the bar line of enrollment would make for a pretty impressive ski slope: After just 27,000 people signed up in the whole of October, The New York Times reported over the weekend, about 100,000 people signed up in November, and then, in the first week of December alone, 112,000 chose plans. The Los Angeles Times put out slightly different numbers Wednesday but agreed on the trend. From an obviously atrocious starting place, enrollment is essentially quadrupling. If that pace were to continue, the 7 million figure would be cleared in March.

I still wouldn’t quite bet on that. But I would definitely and unflinchingly bet on the central proposition I argued last week: By next fall, HealthCare.gov is going to be a net plus for Obama and the Democrats.

Wishful thinking? You can call it that if you want to. But I warn you I’m not usually a wishful thinker. Like most partisans on either side, I tend to expect the worst. It’s usually a wise insurance policy; you’re rarely disappointed. I write such things only when I really think them, like the time in August 2012 when I wrote a column suggesting that Obama could very well win about 330 electoral votes. He won 332, which most anyone else would have said when I wrote that piece was crazy.

I had a hunch then, and I have one now. And my bet is based on a lot more than enrollment numbers. It’s based on the numbers of people who are benefiting and will benefit from aspects of the law. These aren’t in the thousands. They’re in the millions. About 70 million citizens will enjoy free—free—preventive care for a range of services that typically weren’t covered at all before or at best were covered and required a co-pay. About half of them are Medicare recipients (= old people = voters). Preventive care, as you may know, is something our system hasn’t been doing very well. Now it will.

More than 100 million Americans live with what the insurance companies would define as pre-existing conditions. Over these next few months, as their symptoms flare up or especially if they worsen, requiring lengthy hospital stays and intense treatment, they’re going to be seeing that they don’t have to fret about money or whether they’re going to continue to be covered anymore. Mental-health coverage is going to be improved dramatically for up to 60 million Americans. Nearly 7 million senior citizens are going to find in the coming months that they’re no longer screwed by the doughnut-hole prescription-drug problem that was created by the Bush Medicare Part D law of 2003 and corrected by Obamacare. It is saving these 7 million seniors an average of $1,000 a year, which for many of these folks is probably a reasonable chunk of their income.

I could go on. The thing is that all this isn’t going to make the papers and the cable channels much. There isn’t a lot of inherent news value in a free cervical-cancer screening or a prescription-drug refill. But these millions of people live real lives, not on TV, and they and their families and friends will know what has happened.

You see that I’m not making a Beltway/political argument. Washington, D.C., will, I can promise you, be the last city in the United States to change its mind about Obamacare. Once a notion becomes conventional wisdom in this town and rocks a president’s poll numbers the way the disastrous rollout so clearly has, it takes a typhoon to dislodge it. Or a hurricane—remember how Karl Rove was making the United States a conservative country until Katrina came along and sent Bush’s approval numbers down there in the range of curdled milk?

The rollout won’t be a hurricane. It will be a calm rain, a steady shower of reality across the country that may never achieve quite enough force to trump inside-the-Beltway perception but will be strong enough to change many people’s minds around the country.

Fixes still need to be made. But now, as opposed to a month ago, one can feel as if they will be made. And without excusing the bollixing up of the rollout, of which I’ve written very critically, one can also say now that in historical context, this is all happening pretty fast. Remember, the original Social Security legislation was passed in 1935. And when did the first check go out? Not until 1940. Can you imagine a five-year lag in today’s media world? Roosevelt, and more important the program itself, would have been torn to pieces. I think in two more years’ time, and indeed less than that, many millions of Americans will see that what they thought was decent health insurance before the Affordable Care Act was like gaslight before electricity. If that’s wishful thinking, it’s for their sake, not the president’s.