Rohit, Thanks; however your code does not make the entire background that color. There still is a grey "frame" around the colored text.
None of these work:
ActionMenu[ Style["Print Factorials", Background -> Cyan],
{Style["4!", Background -> Red] :> Print[4!]}, Appearance ->
"Frameless", MenuAppearance -> {Background -> Red}, MenuStyle ->
{Background -> Red}]
Am assuming there is an undocumented setting to use; there has to be. ;-)