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.
But others have thought about it in some detail. According to Wikipedia:
Webb did not intend the song to be geographically literal. "A guy approached me one night after a concert [...] and he showed me how it was impossible for me to drive from L.A. to Phoenix, and then how far it was to Albuquerque. In short, he told me, 'This song is impossible.' And so it is. It's a kind of fantasy about something I wish I would have done, and it sort of takes place in a twilight zone of reality."