LOS ANGELES (CNNMoney) -- The next time the White House wants to make a credible defense of President Trump's actions, who should it send to the podium?

The answer is unclear, White House and Washington communications veterans say.

The president is notoriously unreliable. Many of his top aides have demonstrated a willingness to mislead the American people. Others, including Gen. H.R. McMaster and Vice President Mike Pence, have made statements in defense of the president that were later contradicted by the president himself.

The inability of Trump's own spokespeople to speak authoritatively on the president's thinking and actions -- a challenge even Trump himself has acknowledged -- has left the White House with an enormous credibility gap, and has tarnished the reputations of many of its most visible spokespeople.

Facing extraordinary pressure over recent missteps, Trump is now said to be irate with his communications team and considering a shakeup that would result in Spicer's ouster. Kimberly Guilfoyle, a Fox News host, has been telling colleagues (and now the press) that she is in talks to replace him.

Such a shakeup would be unlikely to solve Trump's problem, the political communications veterans said, because Trump himself is the source of the problem.

"This White House as a whole has a major credibility problem, but it emanates from the top," said Rory Cooper, an adviser in the George W. Bush administration. "The buck literally stops there."

"Everyone who comes in contact with Trump is damaged or destroyed by him," said a veteran of the Bill Clinton White House.

Time and again, Trump has forced his aides to defend dubious claims. On other occasions, he has sent his spokespeople and surrogates out in front of cameras without the full details of his thinking.

On a few occasions, he has flatly contradicted them.

Last week, Trump told NBC's Lester Holt he had been planning to fire FBI Director James Comey with or without the advice of Deputy Attorney General Rod Rosenstein. That was several hours after his vice president, his press secretary and other aides said he had fired Comey because of Rosenstein's advice.

In the wake of that mixed messaging, Trump tweeted the explanation: "As a very active President with lots of things happening, it is not possible for my surrogates to stand at podium with perfect accuracy!"

At the end of the week, the White House sent out McMaster, Trump's national security advisor, to take questions at the daily press briefing. It was widely seen as an attempt to deflect attention from the Comey controversy and re-establish some authority at the briefing room podium.

But this week, Trump also contradicted McMaster. On Tuesday, one day after McMaster went before reporters to deny a Washington Post report that Trump had shared sensitive national security information with Russia, Trump tweeted that it was his right to share the information in question.

"I think everyone quite clearly sees that the President isn't serving his staff well, and is likely not open to honest counsel," Cooper said. "So who does that really fall on? Do people blame McMaster for saying something or for the President for putting him in that position?"

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