“The public option, whether we have it or we don’t have it, is not the entirety of health care reform,” the president said. “This is just one sliver of it, one aspect of it.”

For Mr. Obama, giving up on the public plan would have risks and rewards. The reward is that he could punch a hole in Republican arguments that he wants a “government takeover” of health care and possibly win some Republican votes. The risk is that he could alienate liberal Democrats, whose support he will also need to pass a bill.

On Sunday, Senator John D. Rockefeller IV, Democrat of West Virginia, affirmed his support for the public option. “I believe the inclusion of a strong public plan option in health reform legislation is a must,” Mr. Rockefeller said in a statement. “It is the only proven way to guarantee that all consumers have affordable, meaningful and accountable options available in the health insurance marketplace.”

White House officials say the president has not abandoned the idea of a pure government plan, a central feature of the legislation moving through the House. But Ms. Sebelius’s comments did seem to open the door, and at least one Democrat close to the White House said the administration was well aware that, with moderate Senate Democrats opposed to the idea of a public plan, Mr. Obama might have to give up on the notion to get a bill through.

“The president is going to continue to try to persuade everyone of the great value of having a true public plan,” said this Democrat, who spoke on condition of anonymity to avoid discussing strategy publicly. ”But at the end of the day, I believe he recognizes that there are other, arguably less effective, ways to achieve greater coverage, more choice, better quality and lower cost in our system.”