In President Trump’s prime-time address last month declaring U.S. elections vulnerable, his centerpiece claim was that more than 250,000 noncitizens were registered to vote. A day later, the Department of Homeland Security said the striking number covered just four states. New Jersey Gov. Mikie Sherrill already knew her state had a problem but nothing of that scale. The day before Trump’s speech, the Democrat learned from her state attorney general’s office that under the previous governor, the state had accidentally put thousands of noncitizens on its voter rolls. Even worse, hundreds of them appeared to have cast ballots. The governor and her advisers quickly realized…