The committee has requested some evidence by Monday, a senior aide said March 11, AP reported. The request was made in a joint letter from Committee Chairman Representative Devin Nunes and the committee's ranking Democrat, Representative Adam Schiff.
Schiff said in an interview March 12 that he doesn't expect any proof to be produced.
"I don't expect we're going to see any evidence of this either," Schiff told ABC's This Week.
"There are one of two possibilities here. Either the president quite deliberately for some reason made up this charge or, perhaps more disturbing, the president really believes this," Schiff said.
The president's accusations are damaging his own credibility, and the country's, he said. "If six months from now the president should say that Iran is cheating on the nuclear agreement, if he's making that up, it's a real problem. If he's not making it up and it's true, it's an even bigger problem because the question is, would people believe him."
The Trump administration has a history of making claims and failing to provide evidence. Trump and his surrogates have complained of "massive" voter fraud during the presidential election, have alluded to a wave of crimes committed by undocumented immigrants, and seem to have made up or wildly overstated terrorist incidents around the world.
Schiff said the committee will ask FBI Director James Comey to address some of Trump's wiretapping allegations when he comes to an open hearing March 20.
"We're going to be able to ask the director of the FBI among others is there any truth of this? Have they seen any evidence of this? They would be in a position to have to know. And I think on March 20th, if not before, we'll be able to put this to rest," he said.
Schiff pointed out that he doesn't believe the allegations, which many in the previous administration have flatly denied. "I don't think anyone really has any question about this, George. The only question is why the president would make up such a thing."
Comey himself has reportedly asked the Justice Department to publicly deny Trump's allegations.
The president made the allegations over Twitter last week, saying "Terrible! Just found out that Obama had my 'wires tapped' in Trump Tower just before the victory. Nothing found. This is McCarthyism!"
He continued in the same vein for a few more tweets. He has not withdrawn his allegations, and his administration has defended them.
Republican Senators John McCain and Lindsey Graham have both asked Trump to produce some kind of evidence for the explosive accusations, as have hosts of Democrats.