President Trump won't be able to get away with making "outlandish claims" without proof, Rep. Adam Schiff Adam Bennett SchiffOvernight Defense: House to vote on military justice bill spurred by Vanessa Guillén death | Biden courts veterans after Trump's military controversies Intelligence chief says Congress will get some in-person election security briefings Democrats, advocates seethe over Florida voting rights ruling MORE (D-Calif.) said Thursday.

Schiff told CNN's "New Day" that he thinks White House press secretary Sean Spicer and Trump wanted to take the president's claim that former President Obama wiretapped him and "try to bury it in a closed hearing in the Intelligence Committee."

"We're not going to allow that to happen. We're going to air this very publicly," he said.

"And if the president is going to make outlandish claims like this in the future, he needs to know he will be exposed, and high-ranking people within the U.S. government, like the director of our intelligence agencies and the FBI, will be forced to say the president wasn't telling the truth."

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Schiff then cautioned on what could happen if Trump isn't confronted regarding his claim that Obama wiretapped Trump Tower before the presidential election.

"If we don't confront him on this, you can expect he's going to make other equally false claims in the future," he said.

"And this is not only hurting him, but it's hurting the presidency; it's hurting our credibility around the world and this has got to come to an end."

There are questions about whether Trump is "capable of growing with the job," Schiff said.

Trump claimed in a series of tweets early Saturday morning that Obama had wiretapped Trump Tower during the campaign.

Citing no evidence, Trump questioned whether it was legal for a sitting president to tap "a race for president prior to an election."