kgp43, what you have there is a bit of code embedded in the Blix theme.
In that theme’s directory look for the following file: BX_functions.php. This holds the various custom functions the Blix theme puts to use, such as BX_get_recent_posts(), which is the function, or template tag, displaying your recent posts. You can edit the code to correct the issue you’re having with it. In the BX_get_recent_posts() function statement, look for this line:
$posts = $wpdb->get_results("SELECT ID, post_title FROM " . $wpdb->posts . " WHERE post_status='publish' ORDER BY post_date DESC LIMIT " . $limit);
This queries the database to collect your *recent* posts. Problem is, it doesn’t screen out posts dated in the future. To do that, we first add the following right above the quoted line:
$now = current_time('mysql');
Then we change your query to this:
$posts = $wpdb->get_results("SELECT ID, post_title FROM " . $wpdb->posts . " WHERE post_status='publish' AND post_date <= '$now' ORDER BY post_date DESC LIMIT " . $limit);
And that’ll do it.