Phonegap with node.js
Phonegap is a client-side solution only with JavaScript/CSS/HTML running on the browser-app of the phone. The JavaScript Phonegap API talks to the native phone interface and browser interface which gives you options to work natively and as a normal web page would with enhanced permissions. Node.js would only serve you as a data connection for JSON or whatever else you would need to pull/push with a network call.
UPDATE: @Turion had a great comment and made me look a little deeper. Here's what the stack and google came up with:
and direct YouTube link to neu.Node (Node runnning on iphone!!!) http://www.youtube.com/watch?v=xzFH80-HYTo
This might be helpful:
http://phonegap.com/blog/build/phonegap-build-api-for-node/
phonegap-build-api-js is a published NPM module for accessing the PhoneGap Build API with node.js. It abstracts the HTTP communication, deals with the API quirks, and leaves the rest untouched. In other words, it simplifies accessing the PhoneGap Build API, so that you can focus on integrating it with your product.