The speculation that Russian President Vladimir Putin has dirt on President Donald Trump has largely been regarded as a "conspiracy theory," but Monday’s interactions between the two leaders raise questions, according to Axios co-founder Jim VandeHei.

"For those Republicans who want to give the president the benefit of the doubt about his relationship with Russia, it makes any person who watched what they saw say, 'What the heck is going on? Why would the president sit here with Vladimir Putin? He's a thug, a murderous thug,'" VandeHei said Tuesday on CNBC.

White House officials told Axios that they’re "really dumbfounded" by the way Trump handled the Putin meeting. VandeHei said nobody in the administration is really defending or explaining the president’s actions.

Using a carrot and stick analogy, VandeHei said Trump used “no stick at all in a case where it should be all stick or mostly stick.” Putin is a “guy whose enemies end up dead,” he added. “This is a guy whose own government interfered in our elections. This is a guy who's been a constant thorn in the side of U.S. interest overseas."

Trump gave his opponents a “gift,” VandeHei told “Squawk Box” in an interview. “I think most people thought it was a conspiracy theory: [do] the Russians really have the goods on the president. I think until yesterday most Republicans would have to say they didn't think that was the case."

Trump’s performance at Monday’s meeting with Putin was roundly criticized by Democrats and Republicans as well as the media.

In a statement, Sen. John McCain, also the 2008 Republican presidential nominee, called Trump’s news conference in Helsinki “one of the most disgraceful performances by an American president in memory.”

Tuesday on CNBC, Democratic Sen. Mark Warner, vice chairman of the Select Committee on Intelligence, made a similar observation, saying Trump turned in the “weakest performance by an American president ever.”

Other U.S. presidents have made a “similar tactical miscalculation” in trying to forge a better relationship with Putin, said VandeHei, citing as an example former President George W. Bush’s 2001 meeting with Putin. Bush famously said, "I looked the man in the eye” and "I was able to get a sense of his soul.” Bush predicted at the time a “very constructive relationship.”

However, Trump’s continued refusal on Monday to acknowledge the unanimous conclusion by the U.S. intelligence community that Russia interfered in the 2016 election crossed the line “in a sort of an absurd, obvious public way that made the United States deferential to Putin,” VandeHei said.

Trump made America look small, he added. “It’s not that just he looks small and he looks tiny. We do.”

VandeHei said, "I don't think there's any repercussions in the short term. I don't think White House official are going to quit in protest. I don't think Republicans are suddenly going to hold very aggressive hearings on the president and his relationship with Vladimir Putin."

The White House was not immediately available to respond to CNBC’s request for comment on VandeHei’s interview.

VandeHei helped launch Axios in January 2017 after leaving Politico, which he also co-founded and turned into a political powerhouse. Axios has gained a reputation as a place for Washington-related scoops.

Before Politico, VandeHei spent six years as a congressional and White House reporter at The Washington Post and The Wall Street Journal.