Los Angeles County's public health system is once again facing budget deficits that threaten to grow into the hundreds of millions of dollars. A lifeline for many of the county's 2 million uninsured residents, the health system is expected to run a deficit of $344 million during the fiscal year beginning in July. By 2011, the annual deficit is expected to reach $1.2 billion, according to a memorandum issued the health department's interim director.