Bernie Sanders is surging. He trailed Hillary Rodham Clinton by as much as 50 points in the polls a few months ago, but he has pulled within 10 points in New Hampshire, according to some surveys. He has doubled his support in Iowa over the last month. The signs of his support are palpable: Last week, about 10,000 people attended an event in Madison, Wis., and he announced that he raised $15 million in the first three months of his campaign.

But the Sanders surge is about to hit a wall: the rank and file of the Democratic primary electorate.

Senator Sanders is now doing nearly as well as Barack Obama did among liberal voters in 2008. That makes him competitive in relatively liberal contests, like the Iowa caucuses or the New Hampshire primary.

But Mrs. Clinton still holds a huge lead among moderate and conservative Democrats — white and nonwhite alike. Whether Mr. Sanders can close the gap among these voters will determine the seriousness of his candidacy and whether he can pick up more delegates in other primaries. There aren’t many reasons to expect he will break through, and he certainly isn’t doing it yet.