Because she does get an offer of coverage from her employer — and, after turning 65, also qualifies for Medicare — Sebelius would not be eligible for any tax credits buying coverage. But given that she makes just shy of $200,000, chances are she earns too much for that to be a concern.
I dropped a note to Tim Jost, a law professor at Washington & Lee University, and arguably the one human being on this entire planet who knows the Affordable Care Act the very best. He's pretty convinced that, if she wanted to, Sebelius could sign up for marketplace coverage. It would be a pretty crummy financial deal — she would forgo robust employer and Medicare coverage to pay her own way — but it would be legal.
"She could purchase a plan on an exchange since she is lawfully present in the U.S. and not incarcerated," Jost e-mailed. "She could not get premium tax credits both because she has employer coverage and because she is Medicare eligible.
"Of course, like the vast majority of Americans, she is the beneficiary of tax-subsidized employer coverage and it would be remarkable to ask her to give up that to purchase coverage out of pocket with after-tax dollars."
Update: While Sec. Sebelius cited her employer-sponsored insurance ("I would gladly join the exchange if I didn't have affordable coverage in my workplace") as the reason why she could not join the marketplace, a Medicare spokesperson tells Igor Volsky that she also has enrolled in Medicare Part A, which covers hospital trips for the elderly. Health insurers are not allowed to sell Medicare beneficiaries coverage through the marketplace.
This still doesn't make Sebelius ineligible for the marketplaces: Marilyn Moon, a Medicare expert Volsky spoke with, alongside other experts I consulted, believe she could drop her Part A coverage to sign up on the marketplace (instructions on how to do that exist here and here). This would likely be a really poor decision. As Moon tells Volsky, exchange policies don't cover many of the benefits that Part A does. So, enrolling in the marketplaces wouldn't be very smart but, it seems, it could still be legal.