After weeks of battles over aspects of President Obama's proposed health care reforms, the debate focused Monday on one central issue: whether the U.S. government will offer a public insurance option.

The administration stepped back from its insistence on such an option over the weekend, with Obama saying it is "not the entirety of health care reform."

His spokesman, Robert Gibbs, said the president could be "satisfied" without it. And Health and Human Services Secretary Kathleen Sebelius told CNN's "State of the Union" that a public insurance plan is "not the essential element."

The move seemed to be a concession to critics, particularly Republican lawmakers who have assailed the idea of the government playing that kind of role. Yet it also stirred up frustration from those on the left who believe such an option is critical.

Former Democratic Party Chairman Howard Dean, a doctor and one-time presidential candidate, told NBC's "Today Show" on Monday that he believes a public option "is the entirety of health care reform; it's not the entirety of insurance reform."

A petition on his Web site StandWithDrDean.com reads, "A public option is the only way to guarantee health care for all Americans and its inclusion is non-negotiable."

Making the issue negotiable might be a necessity for any legislation to pass through the Senate. Democratic Sen. Kent Conrad of North Dakota, one of six Senate Finance Committee members who have been trying to hammer out the first bipartisan compromise bill, said Sunday a public option simply won't make it through Congress.

"The fact of the matter is there are not the votes in the United States Senate for a public option. There never have been," Conrad told "FOX News Sunday."

Instead of a public option, the negotiators are considering a plan proposed by Conrad to create nonprofit health insurance cooperatives that could negotiate coverage as a collective for their members.

But a bill leaving out a public insurance option could face trouble among Democrats in the House.

"It would be very, very difficult," Rep. Eddie Bernice Johnson of Texas told CNN's "State of the Union," "because without the public option, we'll have the same number of people uninsured. If the insurance companies wanted to insure these people now, they'd be insured."

She added that "an option that would give the private insurance companies a little competition" is "the only way" to be sure that insurance is available to low-income people and people without employer-provided coverage.

Critics suggest that if the government creates an insurance option backed by taxpayer funding, there would be an uneven playing field in the industry. Private insurers wouldn't be able to compete with the government prices, and soon, the government would control a great deal of the health care in America, critics say.

"We have the best health care system in the world," Republican Sen. Richard Shelby of Alabama told "FOX News Sunday." "We need to expand it. We do not need to destroy it."

Supporters of a public option say it will create a badly needed level of competition, ultimately benefiting the public. At a town hall event Saturday in Grand Junction, Colorado, Obama said, "I think that we can craft a system in which you've got a public option that has to operate independently, not subsidized by taxpayers -- it would be nonprofit ... they would have to go on the market and get a market price for capital."

He added, "I think there are ways that we can address those competitive issues."

Though Congress is in recess, the debate has moved forward in public and private ways. At town hall events, lawmakers have made their positions clear and often have been challenged by members of the crowd. And White House spokesman Gibbs said Obama would continue to make calls to lawmakers, even as he vacations with his family.