"This is extraordinary. This is really unprecedented for someone this close to the presidency to criticize the Fed chairman in personal terms, very strident and personal terms. I can't recall any precedent for that," said Greg Valliere, global analyst with Horizon Investments. "I think the markets have to worry about this. I think there's a real chance that he could align himself with the members of Congress that want to sharply curb the Fed's independence."
Peter Boockvar, chief market analyst at The Lindsey Group, agrees the Fed waited too long to hike rates and that it's setting the stage for trouble. "The Fed's running the economy. How can you not discuss the Fed? … It's a tough situation, but the Fed has immersed themselves so deeply in the economy so that any honest discussion of it has to include the Fed. They threatened their own independence by going as far overboard as they have. These institutions were never built to take on these responsibilities," he said.
But as for Trump, if he is elected, he could have problems with the pointed criticism.
"The problem is if he wins, he's opened up this Pandora's box," Boockvar said. "At every single Fed meeting, he's going to be asked, 'What do you think about what the Fed did? What do you think about Yellen's job?' I don't think that's where you want to go."
London-based Capital Economics Tuesday said Trump's criticism could even lead to Yellen's resignation before her term is over.
"If Donald Trump wins November's presidential election, there is now a clear possibility that Fed Chair Janet Yellen would resign almost immediately, perhaps even before the mid-December (Federal Open Market Committee) meeting," Paul Ashworth, chief U.S. economist at Capital Economics, said in a note. "It is hard to see how she could continue in her position until her current term expires in early 2018."
The most critical remarks made about a Fed chairman in recent memory by a president were when George H.W. Bush blamed the loss of a second term on former Fed Chairman Alan Greenspan's policy.
Central banks have been playing a different role since the financial crisis. The world's central banks have used extraordinary policies, including asset purchases and even negative yields, in an effort to boost growth from sluggish levels. The U.S. central bank has not moved to negative yields but it has kept rates near zero for years, raising the Fed funds target rate just once in 10 years. Bankers have complained about the absence of fiscal policy that could fuel growth. Both Trump and his rival Democrat Hillary Clinton propose increasing fiscal spending to boost the economy.
The Fed has been on a rate hiking path, but it has been repeatedly tripped up by the economy and events, such as China's currency devaluation and the Brexit vote. Yellen, who last spoke publicly after the Fed's rate meeting last week, appears before the House Financial Services Committee on Wednesday to discuss regulation and supervision.
"There's a long-standing precedent that presidents or candidates do not speak very critically of the Fed. There's a fairly bipartisan support of the idea that the Fed is not partisan. The Fed takes very seriously its independence," said Michael Hanson, senior economist at Bank of America Merrill Lynch.
Trump has criticized Yellen previously, saying at one point that he would replace her. But in the past he also said he liked low interest rates. During the debate, he voiced some of the same concerns that have been raised by some Fed officials themselves — that the Fed's low interest rates policy runs the risk of contributing to future financial imbalances.
"Believe me, we're in a bubble right now, and the only thing that looks good is the stock market," Trump said during the presidential debate. "But if you raise interest rates, even a little bit, that's going to come crashing down. We are in a big, fat, ugly bubble and we better be awfully careful and we have a Fed that's doing political things."
He also personalized the criticism of Yellen, whose term expires in 2018, a year after the next president takes office.
"This Janet Yellen of the Fed. The Fed is doing political things," said Trump, adding the Fed is letting politics influence its interest rate policy. "Believe me, the day Obama goes off and he leaves and he goes out to the golf course for the rest of his life to play golf, when they raise interest rates, you will see some very bad things happen. Because the Fed is not doing their job. The Fed is being more political than Secretary Clinton."
Amherst Pierpont Securities chief economist Stephen Stanley said the comments lose some of their "shock value" because they were made by Trump, who has taken many unconventional views.
"Without getting into the politics of it, I would think it's a little bit dangerous to say there's a bubble and as soon as rates go up, the stock market is going to come crashing down. For anybody to say that, much less anyone running for president, it is a little bit like shouting fire in a crowded theater," said Stanley. "I think they should have raised rates more than they have. I think that arguing that it's political is obviously more debatable. It's hard to know what the motivation was for the people who are voting, but until proven otherwise, you have to assume they voted in good faith."
Stanley said the market would be concerned if Trump tried to get rid of Yellen were he to be elected president. "I don't know how much capital he would be willing to spend by trying to push her out immediately versus letting her serve out her term. He has professed a certain affinity for low rates. That would be the issue for the markets. … If not Yellen, now who is it going to be," said Stanley.
Yellen appears before Congress on Wednesday a week after the Fed voted to keep rates steady. The Fed is widely expected to raise rates in December. But just as the criticism comes from Trump, there are a growing number of critics within the FOMC. There were three dissents at the last meeting, and one Fed official specifically pointed to concerns about imbalances.
Boston Fed President Eric Rosengren said he favored a gradual tightening "out of concern that not doing so today will put the recovery's duration and sustainability at greater risk, by generating the sorts of significant imbalances that historically have led to a recession."
Yellen may have some comments on the economy but she will largely discuss regulation at the House committee. "I would imagine she'll get some questions on the outlook and policy, and I would imagine she'll echo word for word what she said in her press conference," said Hanson. "In terms of regulation and supervision, there's obviously still stuff up in the air in terms of Basel lll and Dodd-Frank, but I would guess her comments will be very general."
The committee is chaired by Republican Rep. Jeb Hensarling of Texas.
"We're in an election year, so you're definitely going to have people on both sides of the aisle pushing their views and agendas," Hanson said.
There are also several other Fed speakers Wednesday including Minneapolis Fed President Neel Kashkari at 8:45 a.m.; St. Louis Fed President James Bullard makes welcoming comments at a St. Louis Fed community banking conference at 10:15 a.m. EDT; and Chicago Fed President Charles Evans speaks at the same conference at 1:30 p.m. EDT. There are also appearances by Cleveland Fed president Loretta Mester at 4:35 p.m. and Kansas City Fed President Esther George, who speaks at 7:15 p.m.