Under growing pressure, the administration refused repeatedly to state a position Tuesday on legislation formalizing President Barack Obama’s oft-stated promise that everyone who likes their existing coverage should be allowed to keep it under the new health care law.

Senate Democrats spoke dismissively of the proposals, signaling they have no intention of permitting a vote on the issue that marks the latest challenge confronting supporters of the administration’s health care law.

An earlier controversy appeared to be ebbing on a law that has generated more than its share of them. Even so, one strong supporter of the health care law, Sen. Sheldon Whitehouse, D-R. I., good-naturedly told an administration official, “Good luck getting through this mess.”

Whitehouse spoke to Marilyn Tavenner, the head of the agency deeply involved in implementing the law. She had assured lawmakers that initial flaws with the government’s website were systematically yielding to around-the-clock repair effort.

“Users can now successfully create an account and continue through the full application and enrollment process,” said Tavenner, head of the Centers for Medicare and Medicaid Services. “We are now able to process nearly 17,000 registrants per hour, or 5 per second, with almost no errors.”

She encouraged consumers to log onto the site and check it out, and said the administration had estimated that enrollments will total 800,000 by the end of November.

At the same time, she repeatedly refused to tell inquiring Republicans how many enrollments have taken place to date, saying that information would be made available at mid-month.

Tavenner also sought to reassure lawmakers who expressed concerns about cybersecurity at www.healthcare.gov .

Sen. Tim Scott, R-S.C., cited the case of a Columbia, S.C. attorney, who used the website to look for coverage, only to learn later that some of his personal information had been made available to a different browser, a man in North Carolina.

“Has this happened before?” Scott asked. “Can you guarantee that Social Security numbers…are secure? Will you shut down the website, as my friends from the left have already suggested, until security issues are fixed?”

Tavenner offered reassurances, and said officials from her agency were attempting to get in touch with the man whose information had been disclosed.

Scott said what the “consumer sees is not what’s going wrong, it’s that their confidence is going down.”

The controversy over the ability of consumers to keep their existing plans flared last week, when insurance companies mailed out millions of cancellation notices, often citing the new health care law as the reason.

House Republicans intend to vote as early as next week on legislation that permits insurers to reinstate the cancelled plans, which fall short of the coverage requirement under the health care law. One Democrat, Sen. Mary Landrieu of Louisiana, has proposed requiring insurers to do so.

But the Republican leader, Sen. Mitch McConnell of Kentucky, said Democrats had voted unanimously against similar proposals in the past and were having “foxhole conversions.”

“I think what will be really interesting to see in the Senate is the number of Democrats in very red states who are up in ’14 and what they start demanding … in terms of adjustments to this law,” he said.

At the White House, press secretary Jay Carney refused repeatedly to state a position on the proposals, saying he hadn’t “reviewed or seen an examination internally” on any of them.

Shifting the focus away from what Obama has said repeatedly, the spokesman said, “The world back to which many critics want us to go, is a world in which insurers have that power to say that, you know, your relative, who has a pre-existing condition either has no chance of getting coverage or is going to be charged so much that he or she can’t afford it.”

In words Republican critics cite frequently, Obama pledged in mid-2009: “If you like your doctor, you will be able to keep your doctor, period” and “If you like your health care plan, you’ll be able to keep your health care plan, period. No one will take it away, no matter what.”

In recent days, Obama and top aides have sought to amend or clarify the pledge, a tacit acknowledgement that it hasn’t been kept.

Like Carney, Tavenner sidestepped questions on the subject, telling Sen. Lamar Alexander, R-Tenn., and other committee members she hadn’t read the legislation in question.

A few hours later, Majority Leader Harry Reid, D-Nev., showed no enthusiasm for permitting a vote on the measure introduced by Landrieu, who is seeking a new term in what is potentially a difficult race in a swing state. “We’ll have to see,” he said, noting that hundreds of bills are introduced in the Senate each week.

Tavenner took her seat in the witness chair in a different atmosphere from a week ago, when she testified before a House panel and apologized to the public for the poor performance of the website.

This time, Alexander and other Republicans said almost in passing they assume the website woes will be repaired, and focused on areas of cost, cancellation and security concerns.

Sen. Johnny Isakson, R-Ga., displayed a sign behind his seat saying, ‘Tip of the iceberg’ that showed a pale blue iceberg floating in water. Above the waterline, the iceberg was labeled ‘website failures.’ Below were examples of reported health care law problems including canceled coverage, higher co-pay and deductibles, premium increases and fraud and identify theft.

Sen. Lisa Murkowski, an Alaska Republican, said as of Monday, only three people in her state had been able to enroll, and added there were concerns that they had done so on the basis of incorrect information.

Alexander said “Obamacare” had resulted in thousands losing coverage through a state program in Tennessee.

Committee Democrats were less pointed, although Sen. Barbara Mikulski of Maryland cited consumer confusion.

“I think it’s very confusing about where you go,” she said. “I can tell you, people really don’t know, they really, really don’t know.”

There were also expressions of urgency from Democrats.

Sen. Michael Bennet, D-Colo., asked if the website in use in his state could be streamlined.

When Tavenner said she would look into the issue and get back to him, he said: “Can we do that today?”

(AP)