“The main thing for me is the plans that she has that are just more thought out,” she said.

Ms. Warren shows no sign of slowing down on that front. Her campaign is expected to release another major policy proposal within the coming week, timed around a trip to Michigan and Indiana — the 19th and 20th states she will have visited during the campaign’s early stages.

Her proposals have often coincided with campaign trips: an opioid plan before traveling to West Virginia, a proposal to protect public lands before visiting Colorado and Utah, a call to break up big technology companies before a rally in New York City. Altogether, she has posted more than a dozen policy explanations on her Medium page, and T-shirts branded “Warren has a plan for that” have become her campaign’s fastest-selling merchandise.

Ms. Warren’s campaign has also caught the attention of several liberal groups and unions. Top leaders at the Service Employees International Union, the influential labor group with almost two million members, have pointed to Ms. Warren’s ascendance as a reason to slow their primary endorsement process, according to people familiar with the deliberations.

Some leaders at S.E.I.U. wanted to back Ms. Harris early in the primary season, these people said, particularly after her campaign’s strong initial rollout, but the fluid nature of the race has the group’s leaders echoing many rank-and-file Democrats, who feel it is too early to choose sides.

Ms. Warren still faces the long-term challenge of growing her support to include a broader population of Democrats, including nonwhite voters as well as moderates. And she faces obstacles in multiple directions: In addition to competing with Mr. Sanders for voters on the party’s left flank, she faces stiff competition from other candidates to emerge as an alternative to Mr. Biden, whose centrist campaign could appeal to a broad swath of Democratic voters.

Like others in the race, she is dealing with the so-called electability test, as voters assess which candidate they believe is best suited to defeat Mr. Trump — a calculation that can include gender bias in a country that has never elected a female president. Some online supporters have even taken to calling her “Likable Liz” in an attempt to rebuff notions she is only a policy wonk.