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The early problems with the Obamacare rollout have put Kathleen Sebelius, the secretary of health and human services, under pressure to resign or be fired.
The New York Times reported last week that Sebelius was resisting Republican pressure to resign, citing people close to her.
President Barack Obama addressed the Healthcare.gov glitches Monday morning, amid reports that repairs to the site and its infrastructure could stretch into December.
(Read more: Contractors see weeks of work)
A Sebelius spokesperson said Monday that she would testify before Congress about the problems—though the date remains up in the air.