MIDDLETON, Mass. — As the lone Democrat seeking to challenge Elizabeth Warren in the Senate primary in Massachusetts, Marisa DeFranco has been ridiculed, admonished and, worst of all, ignored. But for the moment, Ms. DeFranco, an immigration lawyer with high energy and a scrappy band of volunteers, is enjoying a burst of momentum. She surprised party insiders by collecting enough valid signatures by the May 1 deadline — more than 10,000, gathered everywhere from town meetings to town dumps — to qualify for the Democratic primary on Sept. 6. If Ms. DeFranco clears one more hurdle — winning 15 percent...