(CNN) Some governors responded enthusiastically to President Donald Trump's plan to send the National Guard to the southern border, while others criticized it and suggested they would not comply if directed to send troops from their states.

The governors of the border states of New Mexico, Texas and Arizona -- all Republicans -- expressed their support. But the office of the California governor, a Democrat, did not indicate to CNN whether the governor would back deploying Guard troops.

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In announcing the plan Wednesday, Homeland Security Secretary Kirstjen Nielsen said the administration intended to work "in conjunction with" border state governors. The Trump administration has not approached the plan as a national effort, and said it has reached out only to governors from Southwest border states about deployment.

Mike Lonergan, a spokesman for New Mexico Gov. Susana Martinez, told CNN the governor "​appreciates the administration's efforts to bring states to the table as they go about taking steps to better secure our border." Lonergan added that the governor "fully" supports the men and women of the New Mexico National Guard "in any mission -- state or federal at home or abroad."

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In a news release Wednesday, Texas Gov. Greg Abbott said the Trump administration directive "reinforces Texas' longstanding commitment to secure our southern border and uphold the Rule of Law, and I welcome the support."