The 1934 United States House of Representatives election in New Mexico was held on Tuesday November 6, 1934 to elect the state's at-large representative. Incumbent Dennis Chávez decided not to run for re-election and instead opted to run in the concurrent Senate election. This was the first open seat since 1922. Dempsey prevailed in this open seat by a narrow 4 point margin.

1934 United States House election in New Mexico

← 1932 November 6, 1934 1936 →

Nominee John J. Dempsey Maurecio F. Miera Party Democratic Republican Popular vote 76,833 70,659 Percentage 51.82% 47.66%

County results Dempsey:      50–60%      60–70%      70–80%      80–90% Miera:      50–60%      60–70%

Representative At-large before election Dennis Chávez Democratic Elected Representative At-large John J. Dempsey Democratic