Ms. Warren’s populist message resonates more strongly in New Hampshire than in Iowa. New Hampshire residents, when polled on the specific Clinton and Warren messages, had Ms. Warren within hailing distance of Mrs. Clinton, at 38%-31%. When respondents were asked the sort of question that a campaign might pose—whether they’d vote for Mrs. Clinton, described as close to Wall Street and a supporter of the Iraq war, versus Ms. Warren as a true progressive who stands up to Wall Street—Ms. Warren polled ahead of Mrs. Clinton, at 47% to 42%.

Given that front-runners in primaries typically draw their highest poll numbers at the start of a race, when their name-recognition advantage is most pronounced, Mrs. Clinton’s best hope would be to solidify her current support. Worst case: She suffers the same slippage she did in Iowa in 2008 when she finished a poor third after showing a resounding lead of 58%-12% over then-Sen. Obama.

The implications are clear. Hillary Clinton is vulnerable in the Democratic primaries, something her new adviser Joel Benenson (currently an Obama pollster who previously worked for me) is presumably in the process of finding out. The results from my polling also suggest that potential candidates who would offer populist messages—former Sen. Jim Webb from Virginia and Sen. Bernie Sanders from Vermont—also have the potential to narrow significantly Mrs. Clinton’s current lead.