Thanks pritaeas. I was not quite sure of the Where clause structure so I created a new field called "rec" that is of the auto increment type. This automatically put in this field the values of 1 to 1913. With this serving as a row number, I used it to tell my code which record to update. It worked!

Here is my working code in case it can help someone else solve their problem.

$resultset = mysql_query("SELECT * FROM mailing");

for ($i=0; $i<=1912; $i++)  {
    $r = $i + 1;
    $id = uniqid();
    $query="UPDATE mailing SET id_key='$id' WHERE rec = '$r'";                              
    mysql_query($query) or die ("Error in query: $query <br>" . error_message);
    echo $i . "  " . $id . "<br>";

Your suggestion did get me back on the right track. A BIG THANKS again!