But perhaps most striking is that Mr. Sanders failed to win in Massachusetts — a notably liberal state next to Vermont with a relatively small black share of the vote. Massachusetts residents had the chance to see many of the ads aired by the Sanders campaign for New Hampshire, which is covered by the Boston media market. If Mr. Sanders can’t win in a place like Massachusetts, it is hard to come up with many places where he can.

Mr. Sanders also hoped to fare well in Appalachia, where there’s a large number of working-class Democrats and few black voters. But the results in western Virginia, Tennessee, northern Georgia and Alabama all suggest that Mr. Sanders trails there as well. Perhaps he could still win in Kentucky or West Virginia, but it’s hard to imagine him winning in a landslide if he trails in the bordering regions of northern Tennessee and western Virginia.

Mrs. Clinton decisively won the handful of coal country counties in western Virginia that act as a leading indicator of the results in West Virginia and eastern Kentucky.

Mr. Sanders has big weaknesses among key blocs of nonblack voters: Hispanics, white voters in the South, affluent white voters and older white voters. It would be very hard for Mr. Sanders to win nonblack voters by more than 20 points while facing resistance from any of these groups.

None of this means that the race ends quickly. Democratic delegates are awarded proportionally, so Mrs. Clinton would need time to clinch a majority of pledged delegates. Mr. Sanders has a loyal base of supporters who could easily fund an insurgent campaign well past the point when it is even plausible to suggest he could win the nomination.

But if the race continues as it has to date, Mr. Sanders will suffer serious losses over the next two weeks. Mrs. Clinton could approach or exceed 80 percent of the vote in Mississippi and Louisiana. She could win 60 percent of the vote in Michigan, a state where black voters represent an above-average share of the electorate. Mrs. Clinton would be poised for a clean and decisive sweep on March 15, when five big states with large numbers of black voters — Illinois, Missouri, Florida, North Carolina and Ohio — cast ballots.

Even then, Mrs. Clinton will not have a majority of pledged delegates. Only half will have been awarded. But Mr. Sanders would need to win by around 20 points from that point on to catch up.

The results Tuesday show that outcome is highly unlikely. There is no progressive majority for a “political revolution” in the Democratic Party without the support of black voters.