This is not going to be a complete answer, but I will try and get you started on the right path.
First off, you'll need to use the a filesystem API to download your file to the browser cache. For chrome you can find more info here: https://developer.chrome.com/apps/fileSystem
The API extends through HTML5 though, so you can do this in other browsers as well. See this article for more information: http://www.html5rocks.com/en/tutorials/offline/quota-research/#toc-desktop
Now that is how it works behind the scenes, as far as implementing it yourself, take a look at FileSaver.js
From their Github:
FileSaver.js implements the saveAs() FileSaver interface in browsers that do not natively support it. There is a FileSaver.js demo that demonstrates saving various media types.
FileSaver.js is the solution to saving files on the client-side, and is perfect for webapps that need to generate files, or for saving sensitive information that shouldn't be sent to an external server.
This should allow you to target any modern browser for large file downloading, as well as pausing and resuming downloads.
You may also want to look into NodeJS as there will likely be some packages made already you could leverage in your server application.