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?"
Associated Press writers Josh Lederman, Alan Fram and Ricardo Alonso-Zaldivar contributed to this report.