Right now, dozens of potential therapies — from antivirals to antibodies taken from the blood of coronavirus survivors — are being tested in people. The first results from these studies could come within months if drugmakers enroll the thousands of patients needed to complete the research.

But with the malaria drugs chloroquine and hydroxychloroquine available by prescription from any doctor, and the president touting them as coronavirus treatments at his daily briefings, enlisting volunteers to enroll in clinical trials of other potential therapies may be a tough sell.

Researchers are concerned that clear answers on the efficacy of dozens of other medicines, which will only come from clinical trials, could be delayed by the fervor. Online hype of the malaria drugs, along with the president’s endorsement, is already fueling drug shortages. The FDA added both chloroquine and hydroxychloroquine to its shortage list this week, after prescriptions spiked as much 7,000 percent in March.