"Right now, there's a huge demand for a limited supply, so I just want to encourage people to be patient," said Mayor Sylvester Turner.
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More doses of those vaccines are coming, but meanwhile, other manufacturers could have vaccines this year too.
Johnson and Johnson could have enough data from its phase three clinical trial by the end of the month or early February.
"Benefits of Johnson and Johnson's vaccine, is that it's one dose so that would be a big advantage to have a one dose vaccine. It can also be stored in the refrigerator for up to several months," said Dr. Jennifer Whitaker, assistant professor of Molecular Virology and Microbiology at Baylor College of Medicine.
If it's deemed safe and effective, it could get FDA Emergency Use Authorization by mid-February with millions of doses ready to go.
Then there's also the Novavax vaccine. Baylor College of Medicine is participating in the trial where Whitaker is one of the lead investigators.
"It can be stable in the refrigerator for up to three months. If the vaccine is found effective, it might make distribution and storage a little bit easier," said Whitaker.
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Baylor College of Medicine started enrolling participants in January, and is still looking for people. Enrollment will continue until there are 30,000 participants nationwide.
For more information on the trial you can email COVID-VAX@bcm.edu or call 713-798-4912.
Another vaccine that could have data soon is AstraZeneca.
"We've seen data from trials in other countries and I think they're awaiting the data from U.S. trials," said Whitaker.
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