why not just add the style elements to the <p> tag if that is all you are using it for..
Code:
<div class="cms_widget">
<div class="block">
<div class="cms_widget_header">
<p style="text-align: center; color: white;"><img src="images/cms/widget-blog.png" alt="{vb:rawphrase recent_blog_posts}" /> {vb:rawphrase recent_blog_posts}</p>
</div>
<div class="cms_widget_content">
{vb:raw result_html}
</div>
</div>
</div>