The problem for Obamacare isn’t that people are receiving letters telling them that they’re losing their current health plan. The problem isn’t that HealthCare.gov has been performing poorly since it opened on Oct. 1.

The problem is that those two things are happening at the same time.

If those people with canceled health plans were able to log onto the federal website and find out what their new insurance options were, the outcry over old plans being cut off would likely be tempered. And that suggests that, if the White House can get the website fixed by the end of the month as they’ve pledged to do, the administration might ultimately be able to endure the political firestorm of the last few weeks.

President Barack Obama himself acknowledged that it’s the dual problem of canceled plans and a dysfunctional website that’s led to public frustration with his signature law.

“We should encourage any American who gets one of these letters to shop around in the new marketplace. Now, I recognize that while the website isn’t working as fast as it needs to, that makes it tougher and that makes it scarier for folks,” he told Obamacare supporters on Nov. 4. “We want them immediately to get the information that they need, to understand they’ve got more competition and more options.”

That’s because, as TPM has reported, canceled plans aren’t a bug in the Affordable Care Act — they’re a feature. It was always going to happen. Again, Obama himself has admitted as much in some of his public comments. But that unpleasant public relations reality has been complicated by the fact that a lot of people haven’t been able to access their new options through HealthCare.gov.

Consciously or not, congressional Republicans have tacitly admitted that their best hope in undermining Obamacare isn’t focusing on a broken website, but the health plan cancelations. That’s why some of the House oversight hearings that were ostensibly held to dissect the problems with the website instead centered on the president’s broken promise. That’s why top GOP senators have said that they’re not worried about the website being fixed.

Implicit in that thinking is a fear that, once the website is fixed, people will actually figure out what Obamacare has to offer them. And there is real reason for Republicans to worry when you look at some of the follow-up stories about these people who have ‘lost’ their health insurance.

The initial headline, as in the case of Dianne Barette, is that these people are victims of Obamacare and a violated presidential pledge. But then when the New Republic’s Jonathan Cohn followed up with her, the rest of the story emerged. Once Barette was told that, by logging onto HealthCare.gov, she might be able to find much more robust health coverage that wouldn’t cost her much more than the barebones coverage she has now, she told Cohn that she “would jump at it.”

“Maybe it’s a blessing in disguise,” she said of her canceled policy. As the president’s own comments outlined, that should be the goal for Obamacare’s supporters: To make people like Barette realize what the law can do for them.

Because there is upside for many of these people. But for them to know it, the website must be fixed.