Senator Bernie Sanders, the democratic socialist from Vermont, is waging an improbable presidential campaign, but he won’t disappear after this election. Nor will his followers.

Mr. Sanders probably has no more than a 10 percent shot at winning the Democratic nomination — and that’s if something bad happens to Hillary Clinton or, less likely, if after winning in Wisconsin this week, he scores a huge upset in New York two weeks later and transforms the race.

Yet Mr. Sanders, who for the left wing was a consolation choice after Senator Elizabeth Warren wouldn’t run, has a message that will continue to resonate, especially among the multitudes of young supporters.

The clarity and coherence of the campaign have surprised even those who sharply disagree with him.

“Bernie has run a much better campaign than I ever thought he would,” said Trent Lott, the former Senate Republican leader and Mississippi conservative.