Hillary Clinton's phantom presence in the Democratic presidential-nomination stakes—neither in nor out—is freezing the rest of the field, creating formidable obstacles for other candidates needing to raise money and set up an organization.

When advisers to a fundraising group backing a prospective 2016 Clinton bid came calling in late January, hedge-fund manager and political heavyweight Orin Kramer said he met them in his New York office and agreed to write a check. When another potential candidate, Maryland Gov. Martin O'Malley, tried to reach him, Mr. Kramer said he didn't take the call.

"She's Gladys Knight and all the rest of them are the Pips," said Robert Zimmerman, a longtime Democratic donor, comparing Mrs. Clinton with potential opponents from both parties.

Possible 2016 candidates are in the crucial early stages of raising money, but they won't likely set up formal campaign infrastructures until after this year's midterm elections.

Even though she isn't officially running, Mrs. Clinton retains huge influence with the Democratic Party's fundraising and get-out-the-vote machinery. A super PAC called "Ready for Hillary" is recruiting Clinton campaign volunteers in Iowa, New Hampshire and other early-voting states. A group called Priorities USA Action is prepared to raise millions for her campaign, having made early overtures to donors such as Mr. Kramer.