Take a look at the picture below from my website: www.kokorugs.com
I am using Boostrap and I believe that there are some conflicting CSS styles.
The problem
I use the following CSS and it works for me:
.gsc-input-box input[type="text"], .gsc-input-box input[type="text"]:focus, .gsc-input-box input[type="text"]:active {
-webkit-box-shadow: none;
box-shadow: none;
line-height: normal;
}
line-height: normal;
does the work of removing the text popping out of text box.
I have also documented the fix for Google custom search showing scroll bars in search results tab here: http://www.am22tech.com/google-custom-search-input-box-conflicting-bootstrap-css/