CHAT: proto-language

Hello to the natlang-educated on this list :)

A long time ago I saw a TV program about evolutionary linguistics where a
scientist claimed to have found a word (the meaning had to do with milk,
"to suckle", IIRC) which was common, in variation, to all families of languages;
supposedly this hinted at one original proto-language from which all others
evolved.  Also IIRC, most other linguists seemed to be very sceptical about this
claim.  Does anyone know anything about this?  Do linguists generally think
that language emerged in one place (e.g. if the first Homo sapiens in Africa
had a language) and then spread, or evolved independently in several different
places/times?  Apparently even the Neanderthals had rudimentary language, so
maybe there really was one "original" group of dialects, at least, which are
the great-great-great....-great grandparents of all modern languages?

Thanks,

Josh