UPDATE 1-Deal on U.S. healthcare overhaul still uncertain

* Senators trim price tag of healthcare overhaul proposals

* Only a few Republicans needed, but will they come?

* U.S. Chamber of Commerce mobilizes against plan

(Adds White House adviser David Axelrod, Republican Senate leader Mitch McConnell)

By Donna Smith

WASHINGTON, June 28 (Reuters) - President Barack Obama's drive to overhaul the U.S. healthcare system may be back on track thanks to Senate efforts to cut the price tag to $1 trillion, but a bipartisan deal on the sweeping proposal still is far from certain.

Obama wants changes that rein in the escalating costs of healthcare in the United States and bring insurance to most of the 46 million Americans who currently lack it.

He also wants a bill that the Democrats who control Congress and the Republican minority can support to give a bipartisan stamp of approval to his top legislative priority.

Senate Finance Committee Chairman Max Baucus was upbeat last week after announcing that panel members had found ways to bring the price tag to about $1 trillion over 10 years, down from an earlier estimate of a staggering $1.6 trillion.