Warren avoided taking a stance on whether the individual mandate should be delayed if users continue to experience difficulty with the website.
"Right now, the bad rollout is obviously making a huge difference. There are families who can't get the health insurance that they want," she said. But it looks like progress is being made. We'll just see how long it takes."
Warren acknowledged the problems with the federal exchange, but defended the law itself.
"We need some real accountability for what's gone wrong, but we also need to remember it's a good thing that's being offered here. It's health insurance and it's health insurance now that's available to everyone, no pre-existing conditions," Warren said. "It's a good product, we're just having trouble getting it rolled out and available to people."
President Barack Obama will speak at an event in Boston Wednesday touting the Affordable Care Act.