To clarify, do you mean the widget area that's showing a text widget in the demo at http://themorningafterdemo.wordpress.com/ ?
If so, to get rid of the bottom margin on that widget area, add this to your Appearance → Custom Design → CSS editor:
#feature {
margin-bottom: 0;
}
Note that there is still padding inside various pieces of that widget, including paragraphs and widgets in general. You can remove all of it by also adding this:
#feature p,
#feature .widget {
margin-bottom: 0;
}
These examples apply to the demo site since your site doesn't currently have a widget in the home page feature widget area. If you add a different type of widget, you might have to adjust a different selector in addition to the ones in the examples above, but hopefully you'll be able to see which things to adjust after adding the widget, looking at the page source, and trying out the CSS examples from here.