When using a framework, you will want to take special care to conduct Screen Reader Testing.
If you make accessibility improvements about which you are confident, please help by contributing them to the framework so that those beyond the Stanford community can benefit from your efforts.
This article, Notes On Client-Rendered Accessibility, from Smashing Magazine offers a helpful overview of common accessibility issues (not just for screen reader users) that using a framework can raise.
Also, although JQuery Mobile is not perfect, there are definite efforts to incorporate accessibility. For more, see: jQuery Mobile Progressive Enhancement with HTML5.
See rackt-react-a11y (on Github).