Used to express an action done with extreme intensity or effort, like a blacksmith's hard work. They went at it hammer and tongs trying to meet the deadline.
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Conflict
Often implies a heated argument or confrontation that is fierce and loud. The debaters went hammer and tongs over the issue.
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Informal
The phrase is casual, more likely to be used in informal conversations than formal writing. At the family reunion, they were all talking hammer and tongs.