Mr. Biden’s remark about endorsing the bankruptcy plan came in response to a question about what he would do to engage supporters of Mr. Sanders. The two men will face off one-on-one in a debate on Sunday.

“Bernie and I agree on a whole range of issues,” Mr. Biden said, pointing to subjects including climate change and education, and stressing his willingness to support Mr. Sanders if he is the nominee. Mr. Biden said he also hoped that the choice would be “a matter of alternatives.”

“You know, you may not agree with every detail that I propose, but the fact is that it’s awfully difficult to conclude that I’m anywhere near Donald Trump,” he said.

In its endorsement of Mr. Biden for the Democratic nomination, the statement from the National Education Association cited Mr. Biden’s education plans and said that he and his wife, Dr. Jill Biden — herself a member of the organization — “have consistently reached out to N.E.A. members across the country building the broad support among N.E.A. members.”

The N.E.A. endorsement comes on the weekend before a slate of large, delegate-rich states — Florida, Ohio, Illinois and Arizona — are scheduled to hold primaries. In those states, the organization plans to run a comprehensive outreach effort including digital advertising and to mobilize members to volunteer to support Mr. Biden.

“As president, he is committed to attracting and retaining the best educators by paying them as the professionals that they are as well as increasing funding for support staff and paraprofessionals,” said Lily Eskelsen García, the president of the organization, calling him a “tireless advocate for public education” and “the partner that students and educators need now in the White House.”