Kensuke Nanjo said
According to my daily observation of American English, I think this variant is worth including in pronouncing dictionaries. Quite a few Americans use it and as you may know, this is the second variant for "twenty" in the Merriam-Webster Collegiate Dictionary.There are indeed plenty (“plunny”?) of Americans who seem to pronounce twenty with a seriously backed and lowered quality as compared with their default DRESS vowel.
However, in deciding whether this is a sporadic irregularity found just in this word (and perhaps in plenty too), we must first establish what is their default DRESS vowel. We need to discount the possible effects of what, following Labov, has come to be known as the Northern Cities Vowel Shift.
The “northern cities” (of America) in which this sound change flourishes are clustered around the Great Lakes: places such as Buffalo, Cleveland, Detroit, and Chicago. The geographical extent of the shift varies depending on which vowel is involved and in which phonetic environment(s); and in any case it is also socially and stylistically variable. But what it can do is to make DRESS words sound as if they have the STRUT vowel — perhaps all of them, perhaps particularly those in which the vowel is followed by a nasal. Note that the STRUT vowel shifts too, so that we do not normally get loss of the distinctions exemplified in get – gut, bed – bud, wren – run etc.
So someone who says ˈtwɛ̈ni, with a thoroughly retracted vowel, is not necessarily saying ˈtwʌni (“twunny”), to rhyme with funny.
Others, though, are. They include rirelan, who mentioned
twenty: /ˈtwʌni/ (along with "plenty" /ˈplʌni/. "plentiful" is still /ˈplɛntəfəl/ though.)
Furthermore, Americans from other, mainly southern or western, parts of the country may merge pen and pin as pɪn (i.e. merge DRESS with KIT before a nasal). For them, twenty may rhyme, if not with funny, then with skinny as well as with many.
Kensuke reckons that a reasonably exhaustive pronunciation dictionary ought to give AmE twenty as ˈtwenti, ˈtwʌnti, ˈtweni, ˈtwʌni. Seems reasonable, though perhaps we ought to add ˈtwɪnti, ˈtwɪni, too.