Donald Trump’s political career was born amid the fever swamps of the far Right. He seized on a favourite conspiracy theory bubbling there — that Barack Obama was not, in fact, born in the United States and, therefore, was an illegitimate president — to boost his profile in national politics.

That boost eventually led to his 2016 candidacy. That candidacy led to President Trump. But what never changed is Trump’s willingness to actively engage the world of conspiracy theorists.

The latest example came on Saturday morning when Trump took to Twitter — where else! — to allege that he was the target of a wiretapping campaign authorised by Obama during the 2016 race.

Typed Trump: “Terrible! Just found out that Obama had my ‘wires tapped’ in Trump Tower just before the victory. Nothing found. This is McCarthyism!”

How did he know this, you might ask. When and what government agency told him about the wiretapping, you might ask.

The answer appears to be that Trump made the allegations after reading a Breitbart News article on Friday. That article, based heavily on conservative talk radio host Mark Levin’s views, suggested that the Obama Administration had conducted a “silent coup” to keep Trump from the presidency. Here’s the key paragraph:

“In summary: the Obama Administration sought, and eventually obtained, authorisation to eavesdrop on the Trump campaign; continued monitoring the Trump team even when no evidence of wrongdoing was found; then relaxed the NSA rules to allow evidence to be shared widely within the government, virtually ensuring that the information, including the conversations of private citizens, would be leaked to the media.”

That is not to say that these events could not be related somehow. But it is to say that zero factual evidence has been offered that ties them together.

The White House did not offer that proof on Sunday, demanding instead that Congress add a search for it to its ongoing investigations into Russia’s apparent meddling in the 2016 election. “Reports concerning potentially politically motivated investigations immediately ahead of the 2016 election are very troubling,” White House press secretary Sean Spicer said.

The problem for Trump and his White House is that while they were dodging direct requests for proof of his allegations, people in a position to know were flatly denying the claims.

“A cardinal rule of the Obama Administration was that no White House official ever interfered with any independent investigation led by the Department of Justice,” Kevin Lewis, a spokesman for Obama, said. “As part of that practice, neither President Obama nor any White House official ever ordered surveillance on any US citizen. Any suggestion otherwise is simply false.”

Former director of national intelligence James R. Clapper Jr told NBC’s Chuck Todd on Sunday that “there was no such wiretap activity mounted against the President-elect at the time as a candidate or against his campaign”, adding that he would “absolutely” have been aware if there had been.

Here’s the thing: If you are going to say there is a grand conspiracy that only you and a handful of others see, you need to offer a step-by-step explanation to the broader public to show why you are right.

And that goes double when you have shown a penchant for embracing conspiracy theories — Obama wasn’t born in the United States, Senator Ted Cruz’s father was involved in the assassination of John F. Kennedy, Muslims were cheering on rooftops in New Jersey after the 9/11 attacks, and so on and so forth. The ball is in Trump’s court. Short of convincing evidence to back up the wiretapping claims, the conspiracy-theory candidate will have transformed into the conspiracy-theory president.

Chris Cillizza writes The Fix, a politics blog for The Washington Post, and hosts the Ciquizza podcast, a weekly news quiz