ALBUQUERQUE — Donald J. Trump is unlikely to win the general election unless he improves his dismal standing among Hispanics and women. But his efforts to win over those two crucial constituencies is off to a rocky start.

On Tuesday night, Mr. Trump purposefully attacked Gov. Susana Martinez of New Mexico, who in addition to being the most prominent Hispanic woman in American politics, also happens to be the chairwoman of the Republican Governors Association.

Appearing at a campaign rally in Albuquerque, the largest city in Ms. Martinez’s state, Mr. Trump unleashed a blistering assault on the governor, who skipped the event, by saying she was “not doing the job.”

He faulted her by falsely asserting she was allowing Syrian refugees to settle in the state, and blamed her for Albuquerque’s unemployment numbers as well as the increase in the number of New Mexico residents on food stamps.