Rubio’s numbers have dropped 7 percent since an April survey.
The numbers contrast with a Democratic affiliated Public Policy Polling survey released last week that showed Cruz surging after his 21-hour floor speech against ObamaCare. Cruz closely trails Paul among Tea Party voters, taking 20 percent.
Fifty-eight percent of people say they have not heard enough about Cruz to form an opinion.
On the Democratic side, Hillary ClintonHillary Rodham ClintonConquering Trump returns to conservative summit How the candidates for DNC chair stack up ahead of Saturday's vote DNI official challenges reports of low morale in intelligence community MORE continues to dominate a potential 2016 Democratic primary, with 61 percent of Democrats saying they would vote for her. Vice President Biden takes 11 percent. Those numbers are largely unchanged since Quinnipiac’s last poll in May.
The poll surveyed 1,497 registered voters and has a margin of error of 2.5 percent.