Which group did critics of slavery appeal to, arguing that the peculiar institution ran counter to its interests?

Poor whites.

Explanation:

In the 1850s the economy in the south of the country was thriving due to the increase in the demand for cotton. The growth of this industry, and the lead role that it had in the economy, concerned the businessmen since they needed extra workers. Owing to this demand, a movement in favor of slavery spurred, claiming that international slave trading should be done, again. In response to this movement, abolitionists argued that poor whites should not support slave-trading because it was not beneficial for the people who did not own slaves.