You can do this, but it will take some work. To remove responsive design from Twenty Eleven using the Custom Design upgrade on WordPress.com, you need to do the following:
1. Go to Appearance → Custom Design → CSS and check the option that says, "Don't use Twenty Eleven's CSS, and replace everything with my own CSS."
2. Click the "View the original stylesheet" link and copy all of the original styles.
3. Edit the styles you copied and convert all the url() functions to have complete URLs starting with http:// For example, "url(images/search.png)" becomes "url(http://s2.wp.com/wp-content/themes/pub/twentyeleven/images/search.png)".
4. Find the section in the styles labeled "=Responsive Structure" and remove everything from that section.
5. Save your CSS changes and test the site to make sure everything works as expected.
Note that this is an advanced CSS change. There are only 5 url() references though, so it shouldn't be too hard to find those image references and change them out. You can add "http://s2.wp.com/wp-content/themes/pub/twentyeleven/" to the beginning of all of those image references to make them work.
Also, just to note, I wouldn't recommend removing the responsive design because it's very helpful when viewing from a small device like a phone.