White House economic council director Larry Kudlow said on Thursday that the president was sticking by his decision to nominate Cain "at the moment".
Trump has announced he intends to nominate to political allies - 2012 GOP presidential candidate Herman Cain and Stephen Moore - to get 2 current exemptions to the seven-member Fed board.
Still, the Fed is anxious about the economy overheating and says small, gradual interest rate increases are the best way to tap the brakes a bit to ensure inflation doesn't rise too quickly and bubbles don't form.
Fed officials will conclude a two-day meeting on Wednesday, and Wall Street traders predict almost an 80 percent chance the Fed raises rates a quarter point this week, setting them at a range of 2.25 percent to 2.5 percent.
Kudlow repeated that he disagreed with the Fed's most recent interest rate hikes.
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Powell's appearance Thursday night at a Democratic retreat in Leesburg, Virginia, came as numerous lawmakers gathered there have raised alarms about the Fed's independence in the face of President Donald Trump's frequent criticisms of the central bank. And last week Trump told Reuters that Powell is a "good man" who is "trying to do what he thinks is best", one of the more complimentary statements he's made about the Fed chair in months.
Economists say solid hiring and wage gains that are small from Friday's jobs report for March probably are not enough to change the existing plans of the Federal Reserve to hold off to further interest rate hikes.
Trump, who picked Powell as Fed chairman, has criticized the Federal Reserve's rate increases as it tried to gradually move them to a level that neither brakes nor stimulates growth.
Jeffries, chairman of the House Democratic Caucus and a possible eventual successor to Pelosi, derided Trump's choice of Moore and Cain.
"So, I want to play something for you", she said. "The likelihood is that they will be withdrawn".