WASHINGTON — The most ardent supporters of Senator Bernie Sanders have long been outspoken about their anger toward Republicans — and in some cases toward Democrats. Their idol, the senator from Vermont, has called President Trump a “demagogue” and said recently that he was “perhaps the worst and most dangerous president in the history of our country.”

Now, in Mr. Sanders’s world, his fans have something concrete to grapple with: James T. Hodgkinson, a former volunteer for Mr. Sanders’s presidential campaign, is suspected of opening fire on Republican lawmakers practicing baseball in Alexandria, Va.

That shooting on Wednesday, which wounded four people, may prove to be an unexpected test for a movement born out of Mr. Sanders’s left-wing, populist politics and a moment for liberals to figure out how to balance anger at Mr. Trump with inciting violence.

“Both sides need to look in the mirror,” said Nina Turner, a former Ohio state senator who campaigned for Mr. Sanders and is working on a new think tank started by the senator’s wife. “We have to decide what kind of language we are going to use in our political discourse.”