(Adds comments form Trump, lawmakers and Mnuchin, recasts)
SAN FRANCISCO/WASHINGTON, April 10 (Reuters) - Potential Federal Reserve nominee Stephen Moore extended a remarkable run of commentary on the U.S. economy on Wednesday even as prospects for another possible Fed pick, former presidential candidate Herman Cain, appeared to fade.
People under consideration for jobs at the Fed typically lay low ahead of confirmation hearings by the Senate, but Cain and Moore, both boosters of President Donald Trump and his policies, have followed a different script.
"We can grow this economy at 3 or 4%. Trump wants 5% growth - that might be a stretch," Moore, a senior fellow at the Heritage Foundation, a conservative Washington thinktank, said on Fox Business Network.
Moore has been on at least three conservative radio talk shows this week extolling Trump's economic policies, echoing his view that the Fed's rate hikes last year were a mistake, and laying out his case for a rate cut, which Trump has called for.
The prospect of success for Cain, meanwhile, is looking tenuous, with three Republicans out of the 53 majority in the 100-seat Senate -- Mitt Romney, Lisa Murkowski and Cory Gardner -- saying they would vote against him if he comes up for confirmation, Bloomberg News reported.
A fourth "no" vote for Cain, the former head of the Godfather's Pizza restaurant chain, would doom his chances.
Neither nomination has been formally sent to the Senate but Trump has said he will put their names forward.
Economists and other critics have expressed concerns about two Trump loyalists serving on the traditionally nonpartisan central bank.
On Facebook earlier this week, Cain said the reason he was under attack as a nominee is because he is a conservative. Cain's bid for president in 2012 was derailed by accusations of sexual harassment that he has repeatedly denied.
Cain is "a great guy," Trump said on Wednesday.
"I like Herman Cain," he told reporters. "As to how hes doing in the process that I dont know Herman is a great guy and I hope he does well."
Treasury Secretary Steven Mnuchin also offered some support for the two potential nominees.
"Im not going to make individual comments on individual people, I know Stephen Moore well and I dont know Cain very well, but I have every reason to believe the president supports him and feels strongly, so yeah, I would think he should be confirmed."
Mnuchin also pushed back on concerns about whether their nominations are appropriate.
"I don't think there's any reason whatsoever to be concerned about the independence of the Fed," Mnuchin said. "It's the presidents right and obligation to nominate people to the board. These are two people that the president has confidence in ... they will go through the normal Senate confirmation process."
Moore's projections for U.S. economic growth far outpace the 2% growth most Fed policymakers say is the economy's speed limit over the long term. Moore said he rejected the notion that the U.S. economy could only grow at 2% but acknowledged other countries' economies were softening.
"I am a little bit worried about the global economy," Moore told FBN. "That does restrain growth." (Reporting by Susan Heavey, Ann Saphir, Steve Holland, Pete Schroeder and Trevor Hunnicutt; writing by Ann Saphir Editing by Chizu Nomiyama and Sonya Hepinstall)