TIERRA AMARILLA, N.M. — New Mexico could become the latest state in the American West to place major restrictions on wildlife trapping as frontier ethics and suburban attitudes toward animal suffering collide over the use of steel foot traps and wire snares that many ranchers still swear by.

A Democrat-backed bill that bans traps, snares and animal poison on public land with few exceptions was poised for a crucial vote in in the state House of Representatives as soon as Thursday. Consideration by a less politically progressive Senate would come…