The email template has to be setup to be responsive - so unfortunately there is no default "responsive" setting just because you're using the email editor 2.0.
As such, you'd need to engage with a designer or someone in the know, or use one of the starter templates to achieve a fully responsive design.
That said, some email clients just don't do responsive - for example, Gmail. On the other hand, it's important that you make a best effort to design a responsive template, because some of the most popular email clients do support responsive design very well - for example, Apple Mail.
A tool to test various designs is "Litmus".
If you wanted to follow me and send me a PM I could do you a flat rate responsive design.
The templates that are currently hosted in the Template Picker are responsive and work well on the major email clients. However, you're running into a product limitation that no template can solve. Please see this thread: mktoImgWidth not working in 2.0 email templates
Currently, you'll want to select an image that is either exactly the same size (recommended) as the placeholder image or very very close in height and width (not just aspect ratio). The reason for this is, as you'll read in that thread, whenever you pick a new image, it is overwriting the height/width attribute on the HTML <img> element. If you pick an image that is much different size from the placeholder, you will experience stretching on certain clients. We will be addressing this in the next 1-2 months. But, for now, we and our template partners would recommend you select an image that is the same size as the placeholder.
Also see this thread Which templates in Email Editor 2.0 work with Outlook 2013? which shows renderings of the current templates via Litmus. You'll see that when you use the placeholder images (or an image with an identical size), the email will render nicely on different clients.