WASHINGTON -- Covering the uninsured could take several years, even if Congress passes a bill and President Barack Obama signs it into law this fall, HHS Secretary Kathleen Sebelius said Tuesday.

"Will something probably be phased in? You bet," Sebelius said in a question-and-answer session with The Associated Press. "It won't start the day after the bill passes." It could take until sometime during the next presidential term, which starts in 2013, she said.

A longer phase-in period could make it easier to handle the costs of the bill, which are already prompting second thoughts from some key lawmakers.

Sebelius' comments came after disappointing cost estimates for health care legislation by Sen. Edward M. Kennedy. The Congressional Budget Office released estimates that the bill would cost about $1 trillion over 10 years and only cover about one-third of the nearly 50 million uninsured. Budget officials cautioned that these were early estimates of a bill that's only partly written.

Sebelius discounted the importance of the early estimates, while saying the administration wants to keep the cost at about $1 trillion over 10 years, with about two-thirds of that coming from shifting funds from existing health programs like Medicare and Medicaid.

On a separate and equally problematic issue, Sebelius indicated that the shape of new public insurance plan Obama's been pushing isn't a make-or-break issue for the president.

"It's way too early to say 'This is absolutely in, this is absolutely out,'" she said when asked about it. "I mean, what he's trying to do is get a bill passed."

While Sebelius said the "ballpark" cost for providing full coverage seems to be about $1 trillion, the budget office estimates suggested the price tag could get even bigger.

Costs are becoming a big concern for moderate Republicans the administration is hoping to win over.

Indeed, Sen. Olympia Snowe, R-Maine, on Tuesday said the process that produced Kennedy's bill is "broken."

"We have a fundamental obligation to ensure this legislation does not increase the deficit and, sadly, current congressional health care reform efforts fall woefully short," Snowe said in a statement. Obama also says he wants the bill to be fully paid for.

Stretching out the length of time for providing benefits under the bill could be one way to deal with the cost crunch.

"One trillion is a big number," Sebelius acknowledged. "Frankly, most people have no idea what that means."

The first step in expanding coverage would be to sign up people who are eligible for existing government programs, such as Medicaid and the State Children's Health Insurance Program. HHS is already working on plans to reduce bureaucratic hassles that discourage families from signing up, even if they are qualified for coverage.

After that, it could take until 2011 or 2012 to set up insurance purchasing pools and start covering the rest of the uninsured. The purchasing pools, called "exchanges," would offer a range of private insurance plans as well as a new government option.