WASHINGTON — Judy Shelton, an unorthodox economist who was an adviser to President Trump’s 2016 campaign, could move one step closer to a seat on the Federal Reserve’s Board of Governors this week.While her fate is far from guaranteed, the Senate Banking Committee is expected to approve Ms. Shelton’s nomination on Tuesday, putting her one simple-majority vote in the full Senate away from confirmation at a moment when the central bank is employing vast powers that she has a track record of questioning.Opponents of Ms. Shelton’s nomination say confirming her would place the Fed at risk of politicization while it tried to rescue the pandemic-hit economy. Democrats on the committee have called for a second confirmation hearing in light of the crisis so that they can get her views on the current response.While her nomination seemed shaky in the wake of her mid-February Banking Committee hearing, Republican opposition has slowly crumbled. Senators Patrick J. Toomey of Pennsylvania, Richard C. Shelby of Alabama and John Kennedy of Louisiana were initially skeptical. Mr. Toomey has since said she allayed his concerns, and Mr. Shelby has said he will go along with his Republican colleagues. While Mr. Kennedy has not publicly made up his mind, many analysts saw the scheduling of the vote as a sign of his likely support.Ms. Shelton’s bid can advance to the full Senate without any support from the 12 Democrats on the committee so long as all 13 Republicans back her. Her nomination will come to a vote alongside Christopher Waller’s. Mr. Waller, the research director at the Federal Reserve Bank of St. Louis, was also nominated by Mr. Trump to the seven-seat Fed board. Mr. Waller, a more traditional nominee, is expected to clear the committee easily.Ms. Shelton has become the focus of criticism in part because she flip-flopped on key policy positions after Mr. Trump was elected, moving quickly from supporting higher interest rates to favoring lower ones, in line with the president’s view. She has also questioned the basis of central bank independence.While nominees with close political ties have landed on the Fed board before, Ms. Shelton faces enhanced scrutiny given widespread speculation that Mr. Trump may try to promote her to Fed chair when Jerome H. Powell’s term expires in early 2022.Ms. Shelton also has a long record of supporting a return to the gold standard, which mainstream economists see as a nonstarter because it would be so economically harmful. She recently backed partly away from that position.Sarah Boom Raskin, a former Fed governor and top Treasury official, said in an email: “The economic moment right now is too precarious to be rolling the dice on a person who has not wrestled with the current challenges of managing an economy that has been shocked by a pandemic, and whose views have not been fully articulated or reconciled with prior views.”Ms. Shelton has at times questioned the Fed’s basic functions.In an opinion piece written for The Wall Street Journal in the middle of the 2008 financial crisis, she criticized the practice of allowing interest rates “to be fixed by a central committee in accordance with government objectives.”“We might as well resurrect Gosplan, the old Soviet State Planning Committee, and ask them to draw up the next five-year plan,” she continued. Months later, in early 2009, she led a column with the sentence: “Let’s go back to the gold standard.”At her Senate committee hearing in February, Ms. Shelton said that she “would not advocate” going back to a “prior historical monetary arrangement.” She said that she had looked at historical monetary systems for valuable insights, but that “money only ever moves forward.”She said, however, that having a “stable, level, international monetary playing field” would support free trade.Ms. Shelton was previously confirmed as the United States director of the European Bank for Reconstruction and Development, though she regularly missed the overseas meetings for the international body. She said during her February hearing that she had done so because she had been in Washington for other meetings.Ms. Shelton’s supporters say she would add intellectual diversity to the Fed, with some implying that she might lean against growth in the central bank’s balance sheet — which has expanded as the Fed buys securities and rolls out credit programs to keep markets calm. While she has kept a low profile since the February hearing, Ms. Shelton has occasionally posted comments on Twitter, including on the importance of price stability and on issues related to cryptocurrency.One question that analysts are pondering is what version of Ms. Shelton will show up for work at the Fed if she gets the job: A gold standard proponent, or not? A supporter of low rates, as she has been during Mr. Trump’s administration, or an inflation hawk?“It leaves open the question of what exactly she’d be like on the Fed,” said Sarah Binder, a Brookings Institution senior fellow who has written a book on the politics of the central bank. She pointed out that Ms. Shelton’s out-of-the-mainstream ideas were likely to find little purchase among her colleagues, and that individual governors couldn’t make much of an impact on their own.“You can really imagine her tilting at windmills,” Ms. Binder said.The question of whether Ms. Shelton would become Fed chair-in-waiting seems to be key. Mr. Trump spent 2018 and 2019 publicly criticizing Mr. Powell, though those critiques have tapered off during the current crisis. Should Mr. Trump win re-election, Ms. Shelton could be a potential replacement for Mr. Powell, since governors are often promoted to the leading position.“She could do real damage all on her own as chair,” said David Wilcox, a former research director at the Fed.He also said he worried that she might get in the way of the coronavirus crisis response. “In the moment of crisis, there simply isn’t time to revisit ideas that have been consigned to the dustbin of history,” Mr. Wilcox said.Ms. Shelton would fill a seat that formerly belonged to Janet L. Yellen; the unexpired term would be up for renewal in 2024. Mr. Waller would fill a seat formerly held by Ms. Bloom Raskin, with a term expiring in 2026.While neither nominee would exert much influence as an independent governor, their confirmations would give Mr. Trump his handpicked choices for six of the board’s seven spots. Lael Brainard was appointed governor by President Barack Obama, and although Mr. Powell was named to the board by Mr. Obama, Mr. Trump elevated him to the chair.That stocking of the Fed could also have significant implications for bank regulation, which tends to break more along party lines than does monetary policy. The Powell Fed has been tweaking the rules for the biggest banks around the edges to make them more industry friendly.Ms. Shelton has a long history of pushing for limited regulation. In one 2009 interview, she blamed government intervention in mortgage markets, rather than bad behavior by banks, for the 2008 financial crisis.Mr. Trump previously toyed with nominating Stephen Moore, one of his outside economic advisers, and Herman Cain, a former presidential candidate, to the Fed board, but decided not to after their past comments on and actions toward women came to light.He had earlier nominated a former Fed official, Nellie Liang, to the job, but she faced opposition from the banking industry and eventually withdrew her name. Another nominee, Marvin Goodfriend, also failed to secure the votes necessary for confirmation.