The administration has said that 1 million people visited healthcare.gov before 7 a.m. Tuesday.
"We're thrilled that so many people have paid attention, have visited healthcare.gov. We welcome them to keep coming," Sebelius said.
The site remained inaccessible Tuesday afternoon, as did the websites for several states operating their own insurance exchanges.
Republicans seized on the technical problems to argue that the healthcare law is unworkable.
"The Obama administration should have acknowledged the ample warning signs of problems in the exchanges and heeded the many calls for delay," Sen. Orrin Hatch (R-Utah) said in a floor speech.
Tuesday was the first day to sign up for coverage under ObamaCare. The enrollment window remains open through the end of March. Coverage can take effect as early as Jan. 1 for consumers who sign up by Dec. 15.
"It isn't that you miss something if you don't visit the site today," Sebelius said on CNN.