what does "the Connally-Yarborough feud" mean?
And on the opposite side of the mansion, on West Executive Avenue, Dean Markham had been watching the boarding and the flight with Don Ellinger, a visitor from Texas. “I didn't know O'Brien and O'Donnell were going,” Markham said absently. “Of course,” said the Texan. 'It's a political trip.” He described the Connally-Yarborough feud and added, as the gigantic wasps disappeared into the overcast, “This is a trip the President can't win, no matter what happens.”

Question

what does "the Connally-Yarborough feud" mean?
And on the opposite side of the mansion, on West Executive Avenue, Dean Markham had been watching the boarding and the flight with Don Ellinger, a visitor from Texas. “I didn't know O'Brien and O'Donnell were going,” Markham said absently. “Of course,” said the Texan. 'It's a political trip.” He described the Connally-Yarborough feud and added, as the gigantic wasps disappeared into the overcast, “This is a trip the  President can't win, no matter what happens.”

Answer

John Connally was the governor of Texas, and Ralph Yarborough was a U.S. senator from Texas.  Both men were Democrats, but Connally was fairly conservative (he later became a Republican) and Yarborough was liberal.  There was bad feeling between the men, and they were making it difficult for Kennedy to win Texas in the upcoming 1964 election.  So he and his Texan Vice President, Lyndon Johnson, went to Texas in November 1963 to try to improve the public relationship between the two men and their factions.