A couple of things stand out. Enzi supported Paul’s filibuster. I don’t even remember what the filibuster was about. The other reason that Paul would not like Liz Cheney is foreign policy. They are about as far apart as possible on foreign policy and that is often seen as Paul’s weakness with the Republican base.
RE: I don’t even remember what the filibuster was about.
On March 6–7, 2013, Paul engaged in a talking filibuster to block voting on the nomination of John O. Brennan as the Director of the CIA, questioning Barack Obama and his administration’s use of drones, and the stated legal justification for hypothetical lethal use within the United States.
Paul held the floor for 12 hours and 52 minutes, at times ceding to several other Republican senators as well as one Democratic senator, Ron Wyden, who joined in questioning the use of drones and related topics.
Paul noted the purpose of the filibuster was mostly regarding drone policy, particularly usage on noncombatants on U.S. soil. He argued that the language administration officials had used when questioned over that potential usage of drones was unclear, and could potentially lead to a slippery slope where citizens could be targeted merely for expressing views different from those of the president. He asked the Obama administration to agree that they would not target noncombatants on U.S. soil.
Eric Holder stated in a formal reply that the President DOES NOT HAVE the authority to use weaponized drones within the U.S. to kill, without due process, Americans not engaged in combat. Paul said that he was “quite happy” with the response.
THAT ended the Filibuster.