1. To struggle, fight, resist, etc. I thought we'd have to get the law involved, but he didn't put up much of a fight in the end. I expect they'll put up a fight when we announce the pay cuts, but they'll either have to accept them or look for other work.

2. To make a brave or valiant effort against someone or something, especially when outmatched or unlikely to succeed. Usually modified by the adjective "good." They put up a good fight, but they never really had a chance to defeat us. She and her campaign put up a fight to the very end, but it was clear in the weeks leading up to the election that she would lose.