While Democrats appear overwhelmingly eager for a Clinton candidacy, the poll suggests that the Republican field, at least at this early stage, is far more muddled, with no potential candidate garnering majority enthusiasm for a presidential run.

Thirty-two percent of Republicans say they want Senator Marco Rubio of Florida to run, although Mr. Rubio also seems to have fewer detractors than Mr. Bush or Mr. Paul (more do not know enough about him to say). Only 15 percent of Republicans said they did not want Mr. Rubio to run, compared with 21 percent for Mr. Paul and 27 percent for Mr. Bush. Twenty-four percent said they hoped Senator Ted Cruz of Texas would run, compared with 15 percent who said they did not want him to. Fifty-nine percent do not know enough about Mr. Cruz to say.

The poll did not ask about several other potential Republican candidates, including Gov. John Kasich of Ohio, Gov. Susana Martinez of New Mexico, Representative Paul D. Ryan of Wisconsin and Gov. Scott Walker of Wisconsin. No major candidates in either party have yet declared their candidacy, but several have taken steps indicating that they are seriously considering a run.

On the Democratic side, a majority were unable to offer opinions on some other Democrats seen as potential candidates. When asked about Senator Elizabeth Warren of Massachusetts, 56 percent of Democrats said they did not know enough about her to say whether they would like her to run, as did 59 percent when asked about Gov. Andrew M. Cuomo of New York. Even more, 82 percent, said they did not know enough about Gov. Martin O’Malley of Maryland to say whether he should run in 2016.

Twenty-two percent of Democrats said they would like to see Ms. Warren run, compared with 17 percent for Mr. Cuomo and 3 percent for Mr. O’Malley.