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1. Also, run up against or run into. Encounter something, especially a difficulty, unexpectedly. For example, We didn't know we'd run up against so much opposition, or He ran into trouble with his taxes. [Late 1300s] 2. Work against, as in Public sentiment ran against her. [Late 1300s] 3. Oppose for elective office, as in Susan decided to run against a very popular incumbent. This usage is a figurative application of running in a footrace. [First half of 1800s]
American Heritage Idioms
2
general::
Phrase(s): run against someone
to compete against someone for elective office. • Eisenhower ran against Adlai Stevenson in 1952. • Not many people run against an incumbent., Phrase(s): run against someone or something
Go to against someone or something.
McGrawhill's American Idioms And Phrasal Verbs