Senator Elizabeth Warren used a speech to a grass-roots conference Saturday to take direct aim at Democrats’ diminished moderate wing, ridiculing Clinton-era policies and jubilantly proclaiming that liberals had taken control of the party. While not invoking former President Bill Clinton or Hillary Clinton by name, Ms. Warren sent an unambiguous message that she believes the Clinton effort to push Democrats toward the political center should be relegated to history. “The Democratic Party isn’t going back to the days of welfare reform and the crime bill,” she said, highlighting measures Mr. Clinton signed into law as president that are reviled...