President Biden is planning to make a rare visit to the southern border on Thursday, his press secretary said, traveling to Brownsville, Texas, on the same day that former President Donald J. Trump has already scheduled a border trip.The plans underscore the urgency now propelling Mr. Biden and his team on immigration, which has become one of his most serious political liabilities. Under the Biden administration, record numbers of migrants have crossed the southern border — a fact that Mr. Trump and Republicans have wielded aggressively against Mr. Biden.A majority of Americans…