Votes seen lacking for Obama healthcare program

* 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

By Will Dunham

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.