Hillary Rodham Clinton’s campaign, increasingly worried about the threat of a challenge from Vice President Joseph R. Biden Jr., is making a sudden and urgent effort to throw roadblocks into his path.

After months of voicing doubt about a challenge from the vice president, Clinton campaign operatives are viewing Mr. Biden’s entry into the contest as a serious possibility and are trying to rally the party’s apparatus and its donors to her side. They have flooded uncommitted Democrats with emails, phone calls and a plea for them to sign a letter, a copy of which was obtained by The New York Times. In the letter, Democrats are asked to “pledge to support Hillary Rodham Clinton at the 2016 Democratic National Committee Convention with my unpledged delegate vote.”

A campaign aide said that given the mistakes of Mrs. Clinton’s 2008 campaign, they had always planned to make an early and aggressive push to lock down superdelegate support.

This Saturday, hours before Mr. Biden appears as the keynote speaker at the annual gala of the Human Rights Campaign, the most influential gay and lesbian political group in the country, Mrs. Clinton will have breakfast with the same group. And next Tuesday, former President Bill Clinton will appear on “The Late Show With Stephen Colbert,” after an emotionally powerful appearance by Mr. Biden that became a viral video among some in the Democratic Party.