Gail Wilensky, a senior fellow at Project HOPE who ran Medicare during the administration of President George H.W. Bush, pushed the president for more specifics on how he expects to pay for the plan.
"This is not an easy problem," the president acknowledged. "And it's especially not an easy problem when the economy is going through a difficult phase."
But the president suggested the stars were aligning for reform, citing efforts being made such as the pharmaceutical industry's recent pledge to help defray the costs of prescription drugs for seniors, and argued that now was the time for reform.
"We have to have the courage and the willingness to cooperate and compromise in order to make this happen," the president said. "And if we do, it's not going to be a completely smooth ride, there's going to be times over the next several months where we think health care is dead, it's not going to happen but if we keep our eye on the prize ... then I'm absolutely convinced that we can get it done this time."
Earlier in the day at the White House, Obama told a bipartisan group of governors he wants them to be kept in the loop as health care reform legislation develops on Capitol Hill.
"We're committed to working with them in the weeks and months to come to make sure that when we get health reform done it is in partnership with the states, where the rubber so often hits the road," the president told reporters.
But Obama acknowledged the thorny issues they're all facing -- including whether there should be a government-run public plan, who will pay for it, and how to achieve universal coverage.
"There's no perfect unanimity across the table in terms of every single aspect of reform," the president said.
The biggest bone of contention may be how to pay for reform.
"Anything that we do on health care we have to have a long-term plan to pay the bills," said South Dakota Gov. Mike Rounds, a Republican, who attended the meeting.
In an exclusive interview with ABC News' Diane Sawyer that aired today on "Good Morning America," Obama indicated that there was a breaking point in the balance sheets where he would say that the cost of reforming the system is too great for the federal government to handle, but he did not put a price tag on it.
"I think that if any reform that we get is not driving down costs in a serious way ... if people say, 'We're just going to add more people onto a hugely inefficient system,' then I will say no. Because -- we can't afford it," he said.
One option being considered on Capitol Hill is taxing health care benefits, which are currently tax exempt.
Today, a key Democratic senator indicated that may be inevitable.
"It is hard for me to see how you have a package that is paid for that doesn't include reducing the tax subsidy for health care," said Sen. Kent Conrad of North Dakota, chairman of the Senate Budget Committee, who is regarded among Democrats as something of a deficit hawk.
Conrad sees the potential for a significant source of revenue.
"Tax subsidies for health care. They're huge. Hundreds of billions of dollars a year," he said.
Obama said he opposes that approach, instead wanting to pay for the bill partly by reducing the tax deductions wealthier people can take when donating to charity.