Just a few weeks ago, Joe Biden was fresh off a primary win in South Carolina but had raised less than half as much campaign cash in February as the Democratic presidential front-runner at the time, Vermont Sen. Bernie Sanders.

Big-money groups had sprung up in February to help two of Mr. Biden’s 2020 competitors, and another, Michael Bloomberg, gave his own campaign almost half a billion dollars during the month to gin up support for his long-shot bid.

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