By STEVEN R. HURST President Barack Obama still believes a government-run health care option would best meet his reform goals but is not demanding that it be part of overhaul legislation, White House advisers said Sunday.The White House and lawmakers are trying to blend five House and Senate committee versions of health care legislation into a bill that will pass both houses, where near unanimous Republic opposition was expected.House Democrats are insisting that there be a public option in competition with the private insurance industry to drive down the cost of coverage.