WASHINGTON — Sounding like a frustrated Cassandra, Vice President Joseph R. Biden Jr. lamented last week that Hillary Clinton had not done enough to reach white working-class voters in the presidential campaign. Even more egregious to Mr. Biden, some fellow Democrats had concluded that blue-collar whites were not even worth pursuing.

“I mean these are good people, man!” Mr. Biden exclaimed in an interview on CNN. “These aren’t racists. These aren’t sexists.”

With his typically unambiguous assessment, the vice president thrust himself into a heated debate that has shaped the Democrats’ self-diagnosis since Donald J. Trump won the presidency: Should the party continue tailoring its message to the fast-growing young and nonwhite constituencies that propelled President Obama, or make a more concerted effort to win over the white voters who have drifted away?

For Democrats, the election last month has become a Rorschach test. Some see Mrs. Clinton’s loss as a result of an unfortunate series of flukes — Russian tampering, a late intervention by the Federal Bureau of Investigation director and a poor allocation of resources — but little more than a speed bump on the road to a demographic majority. Others believe the results reflect a more worrisome trend that could doom the party.