Possible Clues:

• Soup du jour, perhaps
• Vidalia, e.g.
• You may cry over it
• Vegetable made into rings
• No one returns after working — it could make you cry!
• Working couple nett minimum of income -- it could bring tears to your eyes
• With 3-Down, deli order
• Peeling one may make a person tear up
• Pair oddly abandoning belief that may lead to tears
• Wambaugh's "The ___ Field"