Many of those close to her believe that the former secretary of state can wait as long as she wants and is best served by delaying her entry in the 2016 race. At this point, an announcement is most likely to come between April and July, people familiar with the matter say.

Some allies and prominent Democrats say she needs to jump in sooner than that and begin raising campaign funds and organizing in states with early contests, even if the payoff means more in the general election than the primaries.

In Iowa, which holds the nation’s first presidential nominating contest, local Democratic leaders caution that Mrs. Clinton risks a backlash if she postpones her announcement too long. Linda Nelson, who leads the Pottawattamie County Democrats, said: “I’ve heard folks who are disgruntled. They’re starting to think: ‘Well, if she’s not going to announce any time soon, I may just start looking elsewhere.’ ”