Would you mind giving this page a read and then letting me know if you still have questions? http://theme.wordpress.com/themes/responsive/
In the Responsive theme, the Call to Action you're referring to is indeed only a part of the home page template, so it sounds like you're trying to do something different from what the default theme options are designed to do. That's no problem, but it wasn't clear from your original question. :)
To make a button similar to the Call to Action button on the Responsive home page template, I would recommend viewing the page source and copying the HTML used for that button into a text widget. The same styling rules that are in place should (mostly) work for the HTML you add compared to the one in the home page template.
I will walk through an example. First, I right-clicked on the "Read more >" button on the Responsive theme's demo page at http://responsivedemo.wordpress.com/ and then I selected the "Inspect Element" option which will pull up the browser inspector. I looked in the HTML that appeared and right-clicked the one with a "call-to-action" class and copied it. Here is the HTML:
<div class="call-to-action"><a href="http://responsivedemo.wordpress.com/about/" class="blue button">Read more ›</a></div>
Note that you can adjust the href value and the link text as needed.
Then I added a text widget and placed that HTML inside it.
http://en.support.wordpress.com/widgets/text-widget/
The padding for links has a more specific rule for the widget area that removes all padding, so to make the new button we added bigger, we need to add that padding back for widgets. Adding the following CSS should do the trick:
#widgets .call-to-action a.button {
padding: 15px 35px;
}
If you're interested in learning more about CSS, please check out this tutorial:
http://www.htmldog.com/guides/cssbeginner/
In the future, would you mind please making a separate help request for things that are separate from the original thread (I know you may not have known it was separate at the beginning this time though). It helps to keep threads from getting too long and makes them easier to search back and find good, past examples.