You're right in that the districts are the ones that set the pay for teachers. But that does not mean the president doesn't have a the ability to change the quality of education.
One of my biggest complaints of bush is his no-child-left-behind bull shit. I went to highschool during the bush admin (yup, I'm still pretty young) and I've seen first hand the failure of the system. I went to a public high school in rural south carolina. Our test scores were one of the worst of any HS in the state, and our state is second worst in the nation on education. So instead of trying to motivate kids by teaching them of the opportunities and value of knowledge, they based the curriculum off of the standardized test scores. The NCLB act caused my classes to no longer focus on practical knowledge, but it became more important that student A who skipped class half the time could pass the standardized exams, then it did to help student B go from a high school graduate to a college student. The bar was significantly lowered, and our rate of diploma to college students dropped. The teachers HAD to lower the bar for everyone to the point that we were only taught what might be on a standardized exam. They had to do this because if they didn't, and us students didn't do as well on the exams, the school would lose funding and have budget cuts, aka, they would have to hire even less qualified teachers. It is currently a viscous circle, and I'm pretty sure if you talk to any teacher at a less than stellar public school they would be glad to voice their opinion on the issue.