American in House backing a Midwest city (5)
I believe the answer is:
omaha
'midwest city' is the definition.
(city in Nebraska)
'american in house backing a' is the wordplay.
'american' becomes 'am' (abbreviation in some contexts).
'in' indicates putting letters inside.
'house' becomes 'ho' (abbreviation for house).
'backing' is a reversal indicator.
'am' placed within 'ho' is 'hamo'.
'hamo' reversed gives 'omah'.
'omah'+'a'='OMAHA'
(Other definitions for omaha that I've seen before include "US city; D-Day 16" , "Largest city in Nebraska" , "American Indian" , "Cotton fabric used for curtains and upholstery" , "Nebraska city and code-named beach of D-Day landings" .)