Texans urged to roll up their sleeves Gov. Greg Abbott and other Texas leaders are rolling up their sleeves to get the COVID-19 vaccine and to encourage the public to follow suit. “I will never ask any Texan to do something that I’m not willing to do myself,” Abbott said before getting vaccinated at a televised event in Austin. The next round of vaccines will go to people 65 and older and to those who are at greatest risk of severe disease and death from COVID-19.