WASHINGTON — The plan was straightforward: After years of being challenged by President Trump and others about a decades-old claim of Native American ancestry, Senator Elizabeth Warren of Massachusetts would take a DNA test to prove her stated family origins in the Cherokee and Delaware tribes. But nearly two months after Ms. Warren released the test results and drew hostile reactions from prominent tribal leaders, the lingering cloud over her likely presidential campaign has only darkened. Conservatives have continued to ridicule her. More worrisome to supporters of Ms. Warren’s presidential ambitions, she has yet to allay criticism from grass-roots progressive...