That claim, which echoes previous promises by Mr. Trump to remove taxes on Social Security, may have come as welcome news for the millions of older and disabled people who depend on the program for income.

The president capped what was arguably the most successful week of his second term with a campaign-style speech in Iowa, where he said the megabill would usher in a period of prosperity. “There could be no better birthday present for America than the phenomenal victory we achieved just hours ago in Congress passing that one big,