WASHINGTON — The Trump administration is struggling to muster the necessary Senate votes to put the conservative economist Marvin Goodfriend onto the Federal Reserve’s board of governors.

Senator Rand Paul, Republican of Kentucky, said Thursday that he would vote against Mr. Goodfriend, who has also yet to attract any support from Democratic senators.

In the narrowly divided Senate, that could be enough to sink Mr. Goodfriend’s confirmation.

The unexpected opposition is a setback for the Trump administration, which has struggled to pick qualified candidates for the Fed’s board. The central bank, which sets monetary policy and plays a leading role in financial regulation, now has just three governors on its seven-seat board, the fewest in the Fed’s modern history.

“Three is really thin,” said Ian Katz, a financial policy analyst at Capital Alpha Partners, a research firm for investors.