Sen. John Barrasso: HHS Secretary Kathleen Sebelius 'The Laughing Stock of America'

As technical problems continue to plague the Obamacare rollout, Senator and orthopedic surgeon Dr. John Barrasso, R-Wy., once again called for Department of Health and Human Services Secretary Kathleen Sebelius to resign.

"She's already, as of 'Saturday Night Live' last night, the laughing stock of America," he said on 'This Week' this Sunday. "She's lost considerable credibility."

Sebelius was parodied in the opening segment of 'Saturday Night Live' last night, poking fun at the failures of the website.

The Obamacare rollout has been beleaguered by problems since the enrollment system went live at midnight on Oct. 1. By mid-afternoon that same day, around 2.8 million people had visited, the federally-run exchange serving 36 states. The resulting system overload meant many visitors were greeted with an error message saying the site was down.

In the following weeks consumers reported problems with system timeouts, creating and logging into accounts and inaccurate information regarding eligibility.

In his weekly address Saturday, President Barack Obama said had been visited more than 20 million times since its launch. However, only around 700,000 Americans have successfully submitted applications.

"The website was supposed to be the easy part of this," Barrasso said on "This Week" Sunday. "This is just the tip of the iceberg of problems, with bigger problems to come."

Joining the discussion from his home state of West Virginia, Democratic Sen. Joe Manchin acknowledged that it was a mistake to go forward with the launch on October 1, but didn't agree that Sebelius's resignation should be part of the solution.

ABC News

"I think she should stay and I think she will get the job done," Manchin told George Stephanopoulos on "This Week."

A Congressional hearing on Thursday revealed that the Centers for Medicare and Medicaid Services allowed just two weeks to road test the website before the launch and was aware in advance of problems that would likely cause system malfunction. Sebelius is due to testify before Congress on the rollout Wednesday.

Frustrations with signing on to the new system have led some on Capitol Hill, including Senate Democrats, to once again call for a delay. Manchin is calling for a one-year delay of the penalty for failing to sign up for the individual mandate. Instead of the current $95 fine taking effect in January 2014, a larger penalty of $325 would hit those not signed up by January 2015.

"It'll still induce people to get involved but it'll also give us the time to transition in," Manchin said.

Earlier this week Sen. Jeanne Shaheen, D-N.H., proposed extending the enrollment period to March 31, 2014. Fellow Democratic Senators Mark Begich, D-Alaska, Mark Pryor, D-Ark., and Mary Landrieu, D-La., who, like Shaheen, are all facing tough reelection bids in 2014, were quick to support the New Hampshire Senator's plan.

The Obama administration announced Friday that private firm Quality Software Services Inc. (QSSI) will oversee repairs to the website, and promised that the portal will be glitch-free and fully-functional by Nov. 30.

Whether this deadline is met or not, Manchin says a transition period is necessary to iron out any other problems with the law, including insuring that policies truly respond to the needs of consumers.

"Nobody should be forced to buy a policy that costs more than what they had and is inferior to what they had," Manchin said. "Those things have to be worked out."

Former Vice President Dick Cheney, who joined Stephanopoulos later in the show, voiced concerns that Obamacare could stifle innovation in the healthcare sector.

"The system we have is the best in the world by far," Cheney said, adding that many of the surgical procedures and devices from which he has benefitted have been gradually developed over several decades.

"What I worry about very much is that the current debate over Obamacare, that Obamacare itself, may damage that innovation machine that we've created out there," he added.

Like "This Week" on Facebook here . You can also follow the show on Twitter here .

Go here to find out when "This Week" airs in your area.