Washington (CNN) The fate of Stephen Moore's ascent to the Federal Reserve Board of Governors appeared in serious question on Thursday as White House officials grappled with a growing opposition from Republican senators .

Conversations were underway in the White House over how to proceed with the bid, according to one official, who said a decision on whether to move forward would likely have to be made by week's end.

Administration officials acknowledged the raft of disparaging comments Moore has made about women extensively reported on by CNN's KFILE , would not likely dissipate. But they said for now -- upon instructions from President Donald Trump -- they were not abandoning the troubled pick.

"We're going to continue to move forward, but we'll review the comments as we see those come out," press secretary Sarah Sanders told reporters at the White House on Thursday morning, appearing to acknowledge the torrent of controversial remarks that have sunk Moore's standing is not likely over.

And on Thursday, Moore told The Wall Street Journal : "I'm not pulling out."

Trump has signaled to advisers that he's intent on naming like-minded individuals to the board of the Federal Reserve, which he has blamed for sabotaging his political prospects by keeping economic growth in check. However, he's also suggested Moore's nomination specifically isn't a battle he's intent on waging.

One person who still appears to support Moore is his chief West Wing backer, Larry Kudlow, the director of the National Economic Council. The President listens closely to his top economic adviser and takes his opinion seriously, part of the reason officials say Moore could potentially remain in the running. Trump and Kudlow have discussed the matter at length in recent days, according to officials.

On Wednesday, Moore -- a former Wall Street Journal editorial board member and CNN contributor -- worked to salvage his position, writing in an op-ed that he was being subject to "scorched-earth battle tactics" by the left.

"I don't take it personally," he wrote in The Hill newspaper . "But it does matter who has a vote on the Fed's Board of Governors, and who will influence the internal debate regarding how it exercises its enormous power."

He then spelled out his views on interest rates and monetary policy -- the purview of the Fed and the subject of intense interest from Trump, who believes his political future could be partially determined by the body.

Sen. Mike Lee, R-Utah, invited Moore to a Senate Republican lunch Wednesday on Capitol Hill to defend himself, but his invitation was scuttled after the White House learned of it, according to a person familiar with how things unfolded.

Moore is being encouraged to keep a low profile because of the drama surrounding his past writings and pending nomination, according to White House and congressional officials. A GOP aide said it was unlikely Moore would meet with senators unless he is officially nominated.

While Trump signaled his intent to nominate Moore more than a month ago, he has not formally submitted the paperwork to the Senate.

JUST WATCHED Trump Fed pick: Critics are 'pulling a Kavanaugh' on me Replay More Videos ... MUST WATCH Trump Fed pick: Critics are 'pulling a Kavanaugh' on me 02:17

On Tuesday, multiple Republican senators expressed reservations to CNN about Moore -- and Republican women appeared to be the hardest sell.

Sen. Joni Ernst, R-Iowa, said Tuesday that she would be unlikely to support Moore if he is formally nominated. Sen. Lisa Murkowski, R-Alaska, acknowledged "reservations" about Moore. And Sen. Shelley Moore Capito of West Virginia said "it's hard to look past" some of Moore's past writings.

The hope among some advisers is that Moore withdraws his name from contention in the same way another Fed Board pick, Herman Cain, did earlier this month . Cain wrote he didn't want to take a pay cut to sit on the board, and Trump tweeted he'd accepted the decision.

Still, past sexual assault and harassment allegations against Cain made it easy for lawmakers to publicly reject his nomination. It became clear soon after Trump announced he would nominate the former restaurant executive to the Fed that he lacked enough support for confirmation.

Moore is a different case. He's is personally close to the President, having advised his campaign and administration. And he built up long-held GOP bona fides and powerful connections as a conservative commentator. Republican senators are wary of putting themselves out as official "no" votes when they are under the firm impression that Moore's nomination will be dead by week's end.

Between six and 10 Republican senators have voiced serious concerns about Moore or told the White House they'd prefer they go another route, according to rough estimates from officials. The nomination will fail if four Republicans join united Democratic opposition.