Obama and is facing up to five years in federal prison.
Prosecutors say Tracy York White, of Las Cruces, entered into a plea agreement Thursday in a Las Cruces court.
White remains in federal custody pending his sentencing hearing, which has yet to be scheduled.
He was arrested last October, days after making the threats.
A criminal complaint alleged that White threatened Obama during an Oct. 24 telephone conversation with an employee of the Social Security Administration in Ohio.
White allegedly threatened to get a firearm, go to the White House and shoot the president.
In his plea agreement, White stated that he made the threats in frustration and knew what he was doing was wrong.