This study will test the effectiveness of etanercept (Enbrel) for treating Sjogren's syndrome-an autoimmune disease that affects the secreting glands. (In autoimmune diseases, the immune system attacks the body's own tissues.) Reduced lacrimal (tear) gland function causes dry eyes with a scratchy sensation, and, in severe cases, vision be may impaired. Reduced salivary gland function causes dry mouth, resulting in greatly increased tooth decay. Dry mouth also makes chewing and swallowing difficult, which may lead to nutrition deficiencies. Sjogren's syndrome can also cause dryness of the skin and of mucous membranes in the nose, throat, airways, and vagina.