In the lyrics, Glen doesn't say where his trip begins. I assume he is leaving from Palo Verde, Goodyear, or Buckeye, Ariz., or somewhere nearby. If he left from further west or south, he would likely be going through Flagstaff or Casa Grande instead of Phoenix.
In any case, he would have to keep his foot on the gas and hope he didn't run into any traffic jams or roadwork, because to get from Phoenix to the Oklahoma border at either Texhoma or Texola within the song's time frame, he would be driving mostly over two-lane highways in 1967.