"I cannot express enough the deep involvement that exists at multiple levels at [HHS] and in the White House to get these things fixed and to get them fixed quickly."
Federal health officials are under intense scrutiny after healthcare.gov's rocky first week.
HHS has slowly improved the website's functionality, blaming the problems on heavy traffic, but the system was still thwarting users' progress as of Tuesday afternoon.
State-based advocates on the call said part of their outreach under the Affordable Care Act is "helping consumers manage their expectations."
Dizzy Warren, community outreach manager at Michigan Consumers for Healthcare, described callers who are "a bit upset" after encountering problems with the enrollment system.
"We've just been listening to people and helping them understand the magnitude of what we're dealing with," Warren said.
"It's important that they understand that it doesn't matter [when you enroll before Dec. 15]. The benefits will all happen at the same time, on Jan. 1."
Oct. 1 marked the beginning of ObamaCare's six-month open enrollment period. Consumers who sign up before mid-December will see their new insurance plans begin in January.
"There is not this huge rush [necessary] for everyone to become enrolled in the first two weeks," Warren said.
"I have not had one caller who didn't calm down … after having that kind of conversation," she said.
Republicans have blasted the problems with healthcare.gov as signs that the Affordable Care Act is unworkable and cast the issues as a massive failure for the Obama administration.
But officials on Tuesday's call stressed that there is strong and wide-ranging interest in the law's new coverage options.
A Kentucky-based advocate said that the state's exchange has enrolled nearly 7,000 people since last Tuesday and that hundreds have received special outreach information.
Barbara Gordon, director of social services with Kentuckiana Regional Planning and Development Agency, said she was surprised by the variety of people who have sought to enroll.
"We've had individuals weeping as they've found out that they or their spouse" were eligible for coverage, Gordon said.