* Key senator says votes lacking for public insurance plan
* Biden says taxing benefits 'wrong way' to pay for reform
* Co-ops touted as possible compromise solution
WASHINGTON, June 14 (Reuters) - President Barack Obama's health secretary on Sunday pushed for a new government-run healthcare program, an idea facing skepticism even in his own party, and a senior Senate Democrat flatly said votes are lacking in Congress for the proposal.
In addition, Vice President Joe Biden opposed proposals being discussed by some lawmakers to tax health insurance benefits provided to people by employers as a way to pay for an overhaul of the $2.5 trillion U.S. healthcare industry.
Obama, aiming to get healthcare costs under control and ensure that the 46 million Americans who are uninsured can get health coverage, wants a new public program to compete with private insurers.
"The president feels that having a 'public option' side by side -- same playing field, same rules -- will give Americans choice and will help lower costs for everybody. And that's a good thing," Sebelius told CNN.
"The president does not want to dismantle privately owned plans. He doesn't want the 180 million people who have employer coverage to lose that coverage. He wants to strengthen the marketplace," Sebelius added.
Healthcare costs undermine the competitiveness of U.S. companies, drive many families into bankruptcy and eat up a growing portion of state and federal spending.
Versions of healthcare legislation unveiled by senior Democrats in the House and Senate include a new government insurance program. But Republicans are adamantly opposed to the idea, saying it could harm private insurers, and some of Obama's fellow Democrats are against it, too.
'VERY GOOD ARGUMENTS'
Kent Conrad, chairman of the Senate Budget Committee, said there is not enough support in Congress for the "public option" even though proponents offer "very good arguments" for it.
"You've got to attract some Republicans as well as holding virtually all of the Democrats together. And that, I don't believe, is possible with the pure 'public option.' I don't think the votes are there," Conrad said on CNN.
There already are large public health insurance programs like the Medicare program for those over 65 and the disabled and the Medicaid for the poor. Obama envisions a program for those not already covered by existing public plans.
Conrad has proposed an alternative to a new public program -- a system of federally chartered insurance cooperatives that could be a nonprofit alternative to the insurance industry.
Susan Collins, one of the few moderate Senate Republicans, said on CNN this was an intriguing idea that could serve as a compromise between those for and against a new public plan.
Obama on Monday is set to address the American Medical Association, which represents the nation's doctors and has voiced skepticism about a broad new public plan but willingness to consider other proposals including the cooperatives.
Sebelius did not embrace the proposal but also did not dismiss it, saying, "There is no one-size-fits-all idea."
Biden, on the NBC program "Meet the Press," also signaled Obama's flexibility on the nature of a new public plan.
Most Americans with health insurance get it through an employer. During last year's presidential election, Obama derided the idea of taxing employer-provided health benefits.
But some lawmakers have revived the idea as a way to paying for the healthcare overhaul. "We've made it clear we do not think that is the way to go. We think that is the wrong way to finance this legislation," Biden said. (Additional reporting by David Alexander and David Morgan; Editing by Eric Walsh)
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