U.S. Department of Health & Human Services (HHS) Secretary Kathleen Sebelius testifies before a House Education and the Workforce Committee hearing on Capitol Hill in Washington, June 4, 2013. (REUTERS/Jim Bourg)
U.S. Department of Health & Human Services Secretary Kathleen Sebelius (REUTERS/Jim Bourg)

Two key Republican lawmakers on Sunday called on Health and Human Services Secretary Kathleen Sebelius to testify before a congressional committee about recent problems with the roll-out of the health-care exchanges required under President Obama’s signature health law. But they stopped short of saying she should resign immediately over the troubles.

Sebelius has declined to appear this week in front of a House committee investigating issues with the federal Web site for the exchange, although she plans to attend a gala in Boston the night before.

Sen. Marco Rubio (R-Fla.) suggested any calls for Sebelius to resign would be premature. "I'm not a big fan of media calls for people to resign, but I think in this case, actions like the one you just outlined will make it harder and harder for her to do her job,” he said on “Fox News Sunday.” “Her refusal to testify and be transparent about it, I think, is undermining her credibility. And there may come a point now, perhaps we're not there today, where she will have to resign."

Sen. Roy Blunt (R-Mo.) said during a later appearance on the show that Sebelius will essentially have no choice but to testify eventually.

"I think the secretary's view that she doesn't have to testify, doesn't have to answer questions, that she's too busy for that, is unsustainable," he said. "She won't be able to sustain it."

"I think she'll have to testify," Blunt added. "I don't think she can refuse to answer questions about this and trying to defend that 'I have time to go to a gala in Boston, but I don't have the time to appear before the Congress because I'm so busy trying to make this system work,' that doesn't make sense and people know this."

Sen. Dick Durbin (D-Ill.) said on the show that Sebelius would eventually testify.