During his first 18 months in office, Trump relied on Treasury Secretary Steven Mnuchin and other economic advisers to pick Fed nominees, but he has wrested control of the process in recent months after blaming Mnuchin for steering him towards Jerome Powell as Fed chairman.
Pelosi went on to accuse Trump of seeking to undermine the Fed's independent role in setting the nation's monetary policy, responding to a question about public comments from Vice President Pence about how Moore and Cain share Trump's views on keeping interest rates low.
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. The Fed approved four interest rate hikes in 2018, continuing a move toward policy normalization that began in 2015.
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.
Economists say solid hiring and wage earnings that are small from Friday's jobs report for March aren't sufficient to change the Federal Reserve's existing intends to hold off on further rate of interest hikes.
Lately, Trump has urged the Fed to cut rates to turn the economy into a "rocket ship".
Powell caused the stock market to rally on November 28 when he added that he thought the Fed had taken rates to "just below" the so-called neutral rate of interest, which is a "Goldilocks" level that doesn't stimulate or contract growth.
Neither Moore nor Cain have been formally nominated by Trump.
Jeffries, chairman of the House Democratic Caucus and a possible eventual successor to Pelosi, derided Trump's choice of Moore and Cain.
"I just don't think of it", said Mary Daly, president of the San Francisco Fed, in an appearance last week on PBS NewsHour.
The pressure has led Democrats to raise concerns that the Fed is being politicised. "The likelihood is that they will be withdrawn". "He's not a political person in any way", she said.