CRC Public Relations is providing media support for Stephen Moore, visiting fellow at the Heritage Foundation and former Club for Growth president who is president Trump's pick for a Federal Reserve Board seat.
Speaking to reporters on Tuesday, Conway said, "I'm a strong successful woman who's worked with Stephen Moore for decades".
"You know, people are talking about women's earnings - they've risen".
Trump's press secretary, Sarah Huckabee Sanders, said Monday that the White House was reviewing Moore's writings and statements but didn't elaborate.
Moore added that "there should be a statute of limitations on saying stupid things", claiming that "times have changed a lot" since he made the comments regarding female income in 2000.
A few hours later, National Economic Council director Larry Kudlow came out to tell reporters that Moore still has the full support of the White House.
During a radio interview last Tuesday, Moore compared himself to Supreme Court Justice Brett Kavanaugh, whose confirmation previous year was marked by allegations he had committed sexual assault as a teenager.
Moore, a 59-year-old conservative political commentator, advised President Donald Trump when he was running for office and has frequently defended him on television news shows.
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But former Fed officials say the choice of Moore, and previously Cain, is a clear deviation toward political partisanship.
Asked about Moore's prospects, Senate Majority Leader Mitch McConnell, R-Ky., noted that the White House has not yet nominated Moore.
The narrow partisan split in the Senate means Trump can only afford to lose four Republicans without closing off any viable path to confirmation if Moore were to be formally nominated. He also argued that women should be banned from refereeing, announcing or beer vending at men's college basketball games. Moore told CNN in an email last week: "This was a spoof".
"They were humor columns, but some of them weren't amusing, and so I am apologetic".
Later Monday, Shelby, the former chairman of the Banking Committee, said he thought the proposed nomination has "some problems" and is causing concern among Republican senators.
Trump's other Fed board pick, Herman Cain, withdrew over past allegations of sexual harassment and infidelity. He said he stands by his economic positions but added if his nomination became too much of a liability to GOP senators, "I would withdraw".
"We're still behind him, and he's going through the process of vetting", Kudlow said Monday.