Updated

The White House on Tuesday refused to state its position on legislative proposals aimed at formalizing President Obama's promise that people who like their existing coverage should be allowed to keep it under the new health care law.

Rep. Fred Upton, R-Mich., and Sen. Mary Landrieu, D-La., introduced bills permitting insurers to reinstate plans that fall short of the coverage requirement under ObamaCare after insurance companies began sending out millions of cancellation letters, often citing the new health care law as the reason.

House Republicans intend to vote as early as next week on Upton's legislation. 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 law.

Upton's legislation permits insurers to sell existing coverage plans that would otherwise be banned under the law, while Landrieu's proposal goes one step further by requiring it.

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, Carney 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."

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.

Senate Minority Leader 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.

Meanwhile, Health and Human Services Secretary Kathleen Sebelius was preparing to return to Capitol Hill on Wednesday for a fresh interrogation on the law, this time from senators with growing concerns about the insurance cancellation notices and the problem-plagued HealthCare.gov website.

Sebelius was due to face questions Wednesday from the Senate Finance Committee, whose chairman, Sen. Max Baucus, D-Mont., was a chief author of the 2010 law and remains a vocal defender. Yet in a measure of its troubled rollout, even he has concerns about the problem-plagued HealthCare.gov website and the potential security risks it poses for consumers' private information.

"I want it all to work, and security is one factor, one component. It has to be secure," Baucus told reporters Tuesday.

At a hearing of the Senate Committee on Health, Education, Labor and Pensions, on Tuesday, Marilyn Tavenner, who runs the agency most directly involved in implementing the health care law, said that nearly 700,000 applications have been submitted at federal and state marketplaces in the law's first month of operation. She said technicians are making improvements that have already made the website faster.

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.

The Assocaited Press contributed to this report.