Yes, this passage does have supporting details to help convince the audience. The passage includes statistics from the Yale School of Public Health that demonstrate the financial benefits of a government funded health care system. This appeals to logos as it uses evidence and logical reasoning to support the argument.
Furthermore, the passage also includes emotional appeals by discussing how government funded health care can benefit families who struggle with financial issues and how it can impact the state by allowing people to focus on their strongest assets. This appeals to pathos as it evokes feelings of empathy and concern for those who are struggling.
The passage also demonstrates the use of ethos by referencing a reputable source like the Yale School of Public Health to support the argument. This appeals to the audience's trust in experts and reliable information.