WASHINGTON — It began on the floor the House, in an impromptu but strikingly testy exchange just before the State of the Union address. Senator Mitt Romney, the Utah Republican known for his party-bucking stands and emphasis on moral rectitude, could be seen scolding Representative George Santos, the New York freshman who faces multiple investigations after fabricating much of his résumé. Mr. Romney admonished Mr. Santos for positioning himself in a prime camera-ready spot in the chamber, saying he didn’t belong there, and had no shame. “I didn’t expect that he’d be standing there trying to shake hands with every...