Is it ensure, insure, or assure?
early 14c., momelen, "to eat in a slow, ineffective manner" (perhaps "to talk with one's mouth full"), probably frequentative of interjection mum. The -b- is excrescent. Meaning "to speak indistinctly" is from mid-14c. Related: Mumbled; mumbling.
1902, from mumble (v.).