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Given county A, I need to know what congressional districts are within it.

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Do you have a platform that you prefer to work on? You could do operations like this in proprietary desktop GIS applications, OpenSource desktop GIS applications, in a scripting language like Python, or as a query in a spatial database like PostGIS. –  DavidF Mar 11 '11 at 4:54
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Based on your description, you are looking for a spatial operation like 'contains()'. You may actually want an operation like 'intersects()' to identify all congressional districts that are fully or partially covered by a county. –  DavidF Mar 11 '11 at 5:06
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The Census has this data here: http://www.census.gov/geo/www/cd110th/tables110.html

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So it appears that it might be a case of counties in congressional districts, rather than the other way around? –  jvangeld Mar 11 '11 at 19:50
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The Congressional Districts and Counties file (census.gov/geo/www/cd110th/natl_code/cou_cd110_natl.txt), lists counties and CD, with one row for each combination. Pair it with the County table here and you should be set: census.gov/geo/www/cd109th/fips_to_cou_name.txt –  neuhausr Mar 11 '11 at 20:02
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