The summer was a rough one for President Biden. Another pandemic surge prompted Mr. Biden, a veteran moderate, to attack Republican governors and embrace vaccine mandates. A bipartisan infrastructure deal hung in the balance. The American withdrawal from Afghanistan, during which 13 service members were killed in a terrorist attack, was criticized as violent and haphazard. But the events left another Biden feeling bruised. “I love him, and it’s hurtful,” Jill Biden said in an interview, the first she has granted to a newspaper since becoming first lady. “I do feel the sting of it. I wouldn’t be a good...