A New York Yankee clinging to Washington come what may (6)
I believe the answer is:
anyway
'come what may' is the definition.
(both can mean 'whatever the circumstances')
'a new york yankee clinging to washington' is the wordplay.
'new york' becomes 'ny'.
'yankee' becomes 'Y' (phonetic alphabet: alpha, bravo, charlie etc.).
'clinging to' indicates putting letters inside.
'washington' becomes 'wa' (abbreviation for the US state).
'ny'+'y'='nyy'
'nyy' placed around 'wa' is 'nyway'.
'a'+'nyway'='ANYWAY'
(Other definitions for anyway that I've seen before include "In whatever manner" , "In any event" , "Still" , "Regardless" , "However that may be" .)