WASHINGTON, June 21, 2009 -- Despite public support for an optional public health insurance plan, President Obama's plan to include one in his health-care bill is facing intensified opposition on Capitol Hill.

The president has insisted on a government-run insurance program that would compete with private companies.

"You will have your choice of a number of plans that offer a few different packages, but every plan would offer an affordable, basic package," the president said in an address to the American Medical Association in Chicago last week. "And one of these options needs to be a public option that will give a broader range of choices and inject competition into the health-care market so that forces waste out of the system and keep the insurance companies honest," he said.

His repeated efforts to pitch that option have met a receptive audience. A New York Times poll released today said that a striking 72 percent of Americans support a public health-care plan, and 57 percent are willing to pay higher taxes to cover all Americans.

Nevertheless, the president's chances for an optional health care plan that would be run by the government may be fading. Republicans and some Democrats have expressed skepticism.

That scrutiny intensified this week after a Congressional Budget Office report found a Democratic plan in the Senate would cost at least $1 trillion over 10 years and cover just one-third of the uninsured.

"The CBO estimates were a death blow to a government-run health-care plan," Sen. Lindsey Graham, R-S.C., said today on ABC's "This Week With George Stephanopoulos."

Republicans have repeatedly hammered the president on the proposal. Sen. Mitch McConnell has taken to the Senate floor daily to lament what Republicans consistently describes as "a government takeover of health care."

Sen. Chris Dodd, D-Conn., who is shepherding a bill through the Senate Health, Education, Labor and Pensions Committee as chief deputy to committee chairman Edward Kennedy, D-Mass., said he still prefers a public option. But Democrats are clearly on the defensive.

"We're not done with this at all," Dodd said today on "This Week." "If this were easy, it would have been done decades ago."

This week, Dodd's committee continues its markup of their version of health-care reform and is expected to consider a proposal for a public health insurance option and a mandate for employers to contribute.

The Senate Finance Committee, which is pursuing its own, private bipartisan health-care effort, has slowed the pace of its closed-door negotiations. It remains unclear if the panel can agree on a plan that covers everyone and pares down the $1.6 trillion price tag, with or without a public option.

Democrats are scrambling to muster support for the president's plan, but even some of them are skeptical.

"Well to be candid with you, I don't know that he has the votes right now," Sen. Dianne Feinstein, D-Calif., told CNN, referring to the president. "I think there's a lot of concern in the Democratic Caucus."