Forcing the title of a text widget on to a new line in the admin area

You can try this custom CSS code to enable multiple title lines for the widgets in the backend:

function custom_css_wpse_98587() {
    echo "<style>
        .widget-top{height:auto !important;}
        .widget-title h4, .widget-title span.in-widget-title{ white-space:normal; }
    </style>";
}
add_action('admin_head-widgets.php','custom_css_wpse_98587');

This is how the widgets show up in my Chrome browser:

Before:

After: