Federal Reserve officials reinforced Friday why this week’s rate cut was so contentious, with one arguing the central bank’s credibility on inflation gives it room to keep easing if the labor market softens and another warning cuts could squander decades of hard-won gains in anchoring price expectations at a low level.

With his approval rating for economic leadership dropping in polls, President Trump has tried to downplay voters’ concerns about affordability. The same problem that tripped up Joe Biden is now dogging Mr.