Members and supporters of UFCW 21 held an informational picket Monday along the sidewalk out front near the main entrance of Mary Bridge.
At issue is the stalled contract negotiations with the 125 unionized nurses that have gone without a new contract since February.
Union Representative Cathy MacPhail said the main sticking point is an effort by the hospital to remove health care benefits from the negotiation table.
"They want complete control," she said.
The next round of talks comes on Tuesday.
UFCW 21 is the largest private-sector union in Washington, with more than 38,000 members working in grocery store, retail, health care, and other industry jobs. UFCW 21 is a chartered member of UFCW International with some 1.4 million workers in North America.