Sen. John Cornyn stood in the shadow of the U.S.-Mexico border wall for a campaign event, but the Texas Republican didn’t offer the kind of diatribe about illegal immigration that stokes his party’s core and fueled Donald Trump’s rise to the White House. Instead, Cornyn, in his courtly Houston drawl, politely thanked Trump for billions in federal dollars to reimburse Texans for work on the wall, praising “the president of the United States, to whom I am very grateful.” Cornyn’s characteristic calm and measured comments betrayed the urgency of the moment for the four-term senator. He’s facing the political fight...