"Don't do this to me."

An exasperated Health and Human Services Secretary Kathleen Sebelius uttered that phrase, caught by a hot mic, to an aide seated behind her at today's House hearing following a contentious exchange with Rep. Billy Long, R-Mo., over whether she should be required to enroll in Obamacare.

More than three hours into the hearing, Long repeatedly pressed Sebelius on why the "architect" of the Affordable Care Act has not voluntarily forgone government-sponsored insurance to purchase a plan through HealthCare.gov, which she is now pitching to millions of Americans.

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"There are a lot of things striking about the roll out of this and about the Affordable Care Act altogether, but the thing that's most striking to me is that when we have the point person for the roll out here, and you're not going into the exchange," Long said.

"Will you tell the American public that, 'Yes, I will go into the exchanges next year like everyone else'?" Long pressed.

"I think it's illegal for me," Sebelius shot back.

"If it's not illegal. If it's legal, will you go in?" Long continued.

"If I have affordable coverage -" Sebelius said before being cut off.

"Come on in, the water's fine," Long concluded.

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As the chairman's gavel sounded, indicating Long's time for questions had expired, Sebelius turned to an aide seated behind her and exchanged words. A hot mic picked up the phrase, "don't do this to me."

She later clarified that she would "gladly join the exchange if I didn't have affordable coverage in my workplace."

But while the secretary suggested it would be "illegal" for anyone with "affordable" employer-provided coverage to enroll in the online exchange, there are no such legal barriers.

According to HealthCare.gov, the government's insurance exchange portal, any American who has coverage through an employer is permitted to "change to Marketplace coverage" at his or her own discretion.

"If you'd like to explore Marketplace coverage options you can, but there are several important things to consider," the site says.

"With most job-based health insurance plans, an employer pays part of your premiums. If you pick a Marketplace plan instead, the employer doesn't contribute to your premiums," it reads. "You should consider this carefully before comparing Marketplace plans."

Still, for Sebelius, who turned 65 earlier this year, it turns out it would be, indeed, "illegal" for her to enroll in the exchanges, even though she didn't know or articulate the reason earlier today.

An HHS spokeswoman said Sebelius is now both in the Federal Employees Health Benefits program and Medicare Part A. The agency says federal law would make it illegal for Sebelius to enroll in any other insurance plan.

"Marketplace plans cannot be sold to a Medicare enrollee, and the secretary is a Medicare enrollee," HHS spokeswoman Joanne Peters told ABC News.

Members of Congress and their staffs are required to enroll in insurance plans through the new exchanges where they will also receive an employer contribution (from the federal government), despite recent Republican efforts to end the subsidy. There is no enrollment requirement for executive branch officials younger than 65, much to the frustration of many congressional Republicans.