WASHINGTON (CNN) -- Go to the Obamacare website today because "it has improved," with more people completing applications after a month of problems that botched the rollout of HealthCare.gov, the official in charge of creating the online program told a Senate committee on Tuesday.



Marilyn Tavenner, head of the federal Centers for Medicare and Medicaid Services, assured the Senate Health, Education, Labor and Pensions Committee the website will be fixed by the end of November, as promised by the administration.

She also said the first figures on how many people have enrolled so far under President Barack Obama's signature health care reforms would be available next week, meeting a mid-November deadline the administration has set.

However, Tavenner had few answers for Republican opponents of the 2010 Affordable Care Act, known as Obamacare, who insisted that the law itself is the problem, not the dysfunctional website for enrolling.

Under tough questioning from GOP senators, Tavenner acknowledged she knew of troubles encountered by consumers, such as a man in South Carolina whose personal details turned up when someone else registered.

In a terse exchange with Republican Sen. Tim Scott of South Carolina, Tavenner said her agency had reached out to the man who complained of the security breach.

"We will find him and we will follow up on his questions," she said, to which Scott offered to provide Tavenner with the man's phone numbers. When she said her agency had the numbers, Scott responded: "He doesn't think so, actually, because no one's called him."

Tavenner replied: "Well, we have a disagreement there."

Later, GOP Sen. Lisa Murkowski of Alaska said that as of October 29, only three people in her state had enrolled and she cited ongoing problems with the system that included providing consumers with incorrect information on available subsidies.

"Are you aware of this? Has it been resolved? Are we working on it?," Murkowski asked. "Because the concern is that not only can people not get on to enroll, but if they do their subsidy calculations are incorrect. "

Tavenner said her staff is aware of the issue and is "working on a fix to the system to correct the Alaska issue specific to Alaska."

In one change to the federal website implemented by tech experts brought in to get it working, Tavenner said consumers can now view and compare health insurance plans online without registering for an account.

When the website came online on October 1, it got overwhelmed by initial volume, and outside contractors working on the system blamed the requirement that people set up an account before they could view coverage options instead of being able to "window shop" without registering.

"In the first few days that we went live, few consumers could create an account," Tavenner said, repeating information she first provided at a House committee hearing last week. "We have now resolved that issue. Users can successfully create an account and go through the enrollment process. We are able now to process nearly 17,000 registrants per hour, or five per second, with almost no errors."

Tuesday's hearing quickly generated the heated rhetoric of the continuing political battle over the Affordable Care Act passed with no Republican support three years ago and upheld by the Supreme Court last year.

Republicans who have made dismantling or repealing the law known as Obamacare a top priority focused Tuesday on policy cancellations and higher prices facing some people, as well as the website woes that included difficulty logging on, error messages and lengthy delays.

Sen. Lamar Alexander of Tennessee, the ranking Republican on the panel, said Obama broke his promise that people who like their previous plan could keep it. Instead, he noted, polices are being canceled for those who buy their own coverage instead of getting it through their jobs or Medicare and Medicaid.

"For these Americans the new promise is, 'if you want health care, go find it on a website the administration says won't be working properly until the end of November,' " Alexander said, calling it "an unwelcome Christmas present."

He called for a proposal to allow people to keep current coverage if they liked it, a concept rejected by the White House.

Democratic Chairman Sen. Tom Harkin of Iowa noted the benefits already in place from Obamacare, and he encouraged Republicans to work on fixing problems instead of trying to undermine the program.

CNN's Lisa Desjardins contributed to this report.

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