The phrase "tough primary battle" refers to a competitive and challenging fight between candidates from the same political party who are trying to secure their party's nomination for an election. Full definition
Three of the four Republican state senators who broke with the party to vote to legalize gay marriage last year faced tough primary battles September 13, and one of those contests turned particularly nasty in the closing days. (wrvo.org)
Akin, who won a tough primary battle this month, has apologized for his comments but also defied pressure to get out of the election. (religion.blogs.cnn.com)
This year, she was in a tough primary battle with New York City Councilman James Sanders and her Senate Democratic colleagues had not been doing much to help her. (nystateofpolitics.com)