That leaves him tied with Sen. Bernie Sanders, the socialist independent senator from Vermont. Given that the poll has a 5 percent margin of error, it's also statistically possible that Biden is actually at 0 percent (again, technically speaking).
Now, to be fair to the VP, this poll is an outlier. It has a very high number of undecideds -- 32 percent -- and 7 percent opt for "no one" (Update: Steven Shepard points out this is because candidate names weren't read to people), which depresses the vote totals for all involved. Even Hillary Clinton has her worst showing in any recent poll, at 48 percent. (She has rarely been below 60 percent.)
In addition, a recent Quinnipiac University poll shows Biden leading the Democratic primary if Clinton were to decide not to run. That's not nothing.
But in all likelihood, Clinton will run. And this is the sixth poll in the last nine to show the vice president in the single digits. Even as Clinton's numbers have come back to Earth, somewhat, Biden isn't looking any stronger.
The reason, as we've written before, is that Biden just isn't seen as very presidential. In fact, only 51 percent of Democrats in a Q poll last year said they thought Biden would make a good president. Among independents, about three-quarters said that he would not.
This new Monmouth poll tells a similar tale. It asked Democratic primary voters to rate each candidate either favorable or unfavorable. The most unfavorable: Joe Biden, at 32 percent. That's about three times Clinton's unfavorable rating (11 percent).
Biden might well run for president. If he does, though, he'll have a huge amount of work to do fixing his brand.