Well, as the
Challenger was an all-coach train, it is much more likely that young star Mr. Presley would have been traveling on the other, all-Pullman half of the train, the
City of Los Angeles. But there is an even better possibility which does not require the train to be late or Mr. Presley's telegram to have been "spiked" for an hour. You see, he would have had to get FROM Memphis TO one of the
CoLA's eastern temini...either Chicago or (enroute) Omaha. And Elvis was coming west from Memphis. Well, through service between Memphis and St. Louis was (rather surprisingly to me!) hard to find, but there was the
Chickasaw operated by the Illinois Central (which also carried through cars from the
Panama Limited) which departed Memphis at 11:15 p.m. the previous evening...although a set-out St. Louis sleeping car could be boarded at 9:30 p.m....and arrived St. Louis at 7:38 a.m. The competing Frisco likewise offered up the
Memphian, bound from Miami, which also departed Memphis at 11:15 p.m. (sleeping cars could be boarded, again, at 9:30 p.m.; there was a four hour layover in Memphis) and arrived St. Louis a minute earlier at 7:37 a.m. The Frisco also offered the all-coach
Sunnyland which departed Memphis at 7:40 in the morning and arrived St. Louis at 3:35 p.m., in time to make the connection; up to you to decide whether young Mr. Presley prioritized his time or his privacy at this stage of his career.
In St. Louis, he would have boarded the joint Wabash/Union Pacific Domeliner
City of St. Louis at 4:15 p.m. This train would stop in Kansas City from 9:10 to 9:40 p.m. (to be complete, Elvis also could have taken the Frisco's
Kansas City-Florida Special to connect in Kansas City; it left Memphis at 7:30 the previous evening and arrived Kansas City at 7:30 in the morning) and then proceeded west over Union Pacific's Kansas lines, stopping in Denver between 8:05 and 8:35 in the morning and also making that same stop in Green River between 4:20 p.m. and 4:40 p.m....just in time to send that telegram.
The
City of St. Louis made a stop in Las Vegas at 7:05 a.m. If Elvis was merely stopping over in Vegas for "a few hours", it's likely that he continued his westbound trip on Union Pacific's
City of Los Angeles (which ran combined with the all-coach
Challenger) which departed Las Vegas at 2:40 in the morning (party hearty, anyone?) and arrived Los Angeles the following morning at 9:30. But who needs sleep at that age?
Edit To Add: Rereading the telegram, I see that Elvis expected to arrive Los Angeles Sunday
afternoon. In that case, he probably stayed in Vegas a full 24 hours and resumed his trip on the next day's
City of St. Louis, which was scheduled to leave Vegas at 7:20 a.m. and arrive Los Angeles at 3:15 p.m. Please note also that while in Vegas Elvis would have been eligible to apply for the "free side trip to Hoover Dam" (see in the notes
here) which Union Pacific offered to all through passengers bound from Eastern cities to California.
Another Edit To Add: Oh, by the way, it was common practice at the time for passengers to send telegrams from trains en route. The conductor and porters carried supplies of Western Union blanks; the passenger would simply fill them out and give them to the conductor. At the next station with a Western Union office the conductor would hand the outgoing messages to the telegraph operator and they would be sent out (probably by Teletype rather than Morse Code at a major station in that era, although Morse was still in use on branch lines into the 1960s). Telegrams could also be sent
to passengers on trains; see my comments on
this page for the procedure and also a link to the reference from which it was taken.