I haven't used PhoneGap yet, but they claim that you develop apps with plain old JS, CSS, and HTML.
If that's true, then use the API just like you would from a web page -- with simple AJAX calls.
Here's a working example (using jQuery):
var userID = 1416412;
var pageNum = 1;
var pageSize = 100;
var siteParam = 'stackoverflow';
var appKey ...
For one use the current API version (2.1) instead of an old one (1.1 in your case).
The API expects JSONP requests to specify the callback as the jsonp parameter, not the callback that jQuery uses by default.
While really you should consider upgrading to API 2.1, which does expect callback (and allows CORS, for that matter), you can fix your code by putting in the jsonp parameter placeholder: