Schiff, the chairman of the House Intelligence Committee, is not a credible figure in the probe, Benson said Friday on "Special Report."
"The main story is 'what the president did,' 'what the president said,' and 'why he did and said those things'," he said.
"I think it's smart... if you're from the White House perspective in terms of how to fight back on this, to make Schiff front-and-center. I don't think he is a credible person."
Benson, a Fox News Radio host, claimed the southern California lawmaker has been dishonest on occasion and is a "lightning rod" in Congress.
"To focus a lot of the response onto him is wise," he said.
However, Benson also said the White House still has serious questions to answer about the Ukraine situation.
"I'm very much ready for the weekend and I suspect the president might be too," he added.
Earlier Friday, sources told Fox News the intelligence community whistleblower who alleged misconduct at the White House over Trump’s call to the Ukrainian president did not disclose contact with Schiff’s staff to the intelligence committee inspector general (ICIG).
The sources said ICIG Michael Atkinson told lawmakers in a closed session that the whistleblower did not disclose the contact with the California Democrat's committee and that Atkinson didn’t investigate that contact as he had no knowledge of it.
In a statement after the hearing with the inspector general, Schiff ripped into Republicans, saying they have “continued the president’s strategy of deflection by making the absurd claim that because a whistleblower contacted the committee seeking guidance, the committee cannot conduct an investigation into the complaint.”
Fox News' Catherine Herridge and Adam Shaw contributed to this report.