President Obama has expressed disappointment about the problematic start of the individual mandate and has vowed to solve the issues.
"I think that the administration is working deeply on the problems that exist," Burwell said on Bloomberg television's "Political Capital with Al Hunt."
"I am optimistic that we will continue to make progress on that issue."
Burwell also is focused on the start of a House-Senate budget conference and said that the president will remain engaged in negotiations.
She said she hopes that Congress and Washington policymakers will weigh the negative effects on the economy of the 16-day shutdown as they head into the conference and subsequent fiscal decisions.
"I think we're hopeful, and we see signals on a bipartisan basis that a shutdown is no longer on the table," she said.
Burwell said, "we're hopeful that many issues can be on the table, both big and small" that include long-term deficit reduction, which includes buying out the sequester, and possibly deal with corporate tax reform.
She said president's budget for fiscal 2014 includes deficit reduction of $1.8 trillion over 10 years, $1.2 trillion of that would cover the costs of the sequester with an extra $600 billion in revenues.
"To do those kinds of changes in long-term changes, we believe you have to think about it in a balanced way over time and include not just entitlements, but also revenue," she said.
Congressional Republicans have argued that the $1.2 trillion in deficit reduction is already going to happen because of the spending cuts included in the sequester and shouldn't be claimed by the White House.
She said the budget conferees could consider a 10-year deal that includes some of these big issues or they can think about a smaller approach, and that would be a year or two.
"I think either are possible. And I think what we've seen in the last weeks, in the last month is, one, you actually can't predict exactly what will or will not happen in terms of where people will go and what you can get," she said.
"So I think what we need to do is go in with optimism, put everything on the table, and see how far we can take moving the economy forward using fiscal policy.”