It remains to be seen whether the two men will inspire and animate a powerful moderate coalition in a way that Mr. Biden has not, or splinter the party’s less-liberal constituencies and effectively strengthen Ms. Warren or Mr. Sanders. Or, they might just find themselves entirely superfluous in an already crowded field.

“We have several moderates in the campaign now, but they’ve not been able to fill the lane,” said Marlon Kimpson, a state senator in South Carolina who has been hosting town hall-style events with presidential candidates. “Now, you’ve got all these people wanting to dip their toe in the water and test the likelihood that they can fill this role.”

Mr. Kimpson said Mr. Biden was still the most natural option for moderate voters, but warned that voters “don’t seem to be very motivated about his candidacy.” He said he was skeptical that either Mr. Bloomberg or Mr. Patrick could do better with such a delayed start, though he considered Mr. Patrick as by far the more intriguing option.

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“I think Deval Patrick makes an excellent candidate, however, I am very, very concerned that he simply will not have enough time to make the case in the state of South Carolina,” Mr. Kimpson said, adding of Mr. Bloomberg, “We are familiar with him, but there doesn’t appear to me to be any excitement about his potential.”

Among the other Democratic campaigns, there is more confusion than consensus about what effect Mr. Patrick and Mr. Bloomberg might have on the primary, beyond straining the fund-raising efforts of other candidates who appeal to the business community. That could be an acute challenge for Mr. Biden, the only leading candidate who has been facing a significant cash crunch in recent months, as well as all of the less-prominent candidates hoping for a late breakthrough.

Neither of the two newcomers has done anything to build an operation in the early primary states, and Mr. Bloomberg has indicated he plans to skip those four February contests entirely. Any major effect they will have on the nomination fight would likely come in the states that vote after Iowa and New Hampshire, where the race is less defined.