Nunes compared the proceedings against President Trump to "three-card monte" and the medieval Inquisition.
Democrats like committee Chairman Adam Schiff, Nunes claimed, promised a fair hearing, but have not yet delivered.
"What have they delivered? The impeachment version of three-card monte, the notorious short-con card trick where the mark -- in this case President Trump and the American public -- stands no chance of winning," he said.
"The Democrats promised the whistleblower's testimony -- in fact, they told us we need to speak with the whistleblower."
Nunes said Democrats' plans changed when reports surfaced that Schiff's staff had been in contact with the Ukraine whistleblower.
Nunes then offered three statements he considered popular legal axioms: "If the facts are against you, argue the law. If the law is against you, argue the facts. And, if both are against you, pound the table and yell like hell."
He claimed the Democrats are using a fourth "tactic" -- "If the facts and the law are against you, simply rig the game and hope your audience is too stupid to catch your duplicity."
Nunes went on to claim the impeachment inquiry reminded him of the Middle Ages when inquisitors were able to bring a charge against someone without affording them due process.
After Nunes concluded his remarks, he yielded the floor to Schiff, D-Calif., as required by House procedure, but not before making a quick dig at his rival.
"I now yield to Mr. Schiff for 'Storytime Hour,'" the ranking member said.
Schiff smiled and deadpanned, "I thank the gentleman -- as always -- for his, uh, remarks," a comment met by loud laughter in the hearing room.