Updated 10/21/2013 at 5:37pm
Washington (CNN) - Republican gubernatorial nominee Ken Cuccinelli of Virginia joined a host of other Republicans calling for President Barack Obama to fire Health and Human Services Secretary Kathleen Sebelius for the rocky enrollment process for Obamacare.
"If President Obama is serious about cleaning up the mess he's created, he'll immediately fire Secretary Sebelius and call on Congress to pass legislation to delay the individual mandate," Cuccinelli said at a campaign event Monday, according to prepared remarks.
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In 2010, Cuccinelli became the first state attorney general to file a lawsuit challenging the constitutionality of the health care law. The Supreme Court upheld the law in a ruling last year.
In recent days however, Cuccinelli seemed to back away slightly in his criticism of Obamacare during the partial government shutdown, calling it "the law of the land" and asking members of Congress to pass a short-term spending bill that would bring the shutdown to an end.
But he added at the time: "It doesn't mean that it's all done and we are set and over with it...They don't even know how they are going to implement it. We are learning a lot as we go here."
During the event, Cuccinelli was ambivalent on the vote last week to end the government shutdown and raise the debt ceiling. "I don't know whether I would have voted for it," he said.
State and national Democrats pounced on that statement.
"Ken Cuccinelli's clear opposition to the bipartisan agreement that reopened the federal government confirms what voters have learned: he will always stand up for his extreme, Tea Party ideology over the needs of the people of Virginia," Democratic Governors Association Executive Director Colm O'Comartun said in a statement.
With a little more than two weeks before Election Day, Cuccinelli finds himself behind in the polls to his Democratic opponent, Terry McAuliffe.
The president on Monday addressed the technical problems associated with the Obamacare website, where people have had trouble applying for insurance on the state exchanges since they opened up on October 1.
Obama acknowledged that HealthCare.gov "hasn't worked as smoothly as is it was supposed to work," but added that "thousands of people are signing up and saving money as we speak."
Sebelius was called to testify by a congressional committee in the GOP-controlled House this week about the website debacles, but Sebelius' staff said she would be unavailable on Thursday, the date of the hearing.
But the Senate's No. 2 Democrat said Sunday Sebelius will likely testify at some point.
“Ultimately, Secretary Sebelius will testify,” Sen. Dick Durbin, D-Illinois, said on "Fox News Sunday."
Obama's administration said over the weekend nearly half a million people have applied for health insurance this month, and they've vowed to fix the technical issues on HealthCare.gov.
"I think there is no one more frustrated than the President at the difficulty in the website," Treasury Secretary Jack Lew said Sunday on NBC's "Meet the Press." The Department of Health and Human Services "has got plans to fix this, and they have to fix this. It has to be done right."
- CNN's Rachel Streitfeld, Paul Steinhauser, Tom Cohen, Laura Koran, and Kevin Bohn contributed to this report.