Hi. I had the same problem, events for January 2014 not showing up, and here's what I did.
Edited the file: /wp-content/plugins/events-manager/em-wpfc.php
After this line:
$month = date ( "m", $tomorrow );
$currentMonth = date ( "m", $_REQUEST ['start'] );
if($currentMonth=="12" && $month=="01")
What it does is if current $month is = 12 "December" and $tomorrow's month is 01 "January" then increase the Year.
I know this is not the best solution, but the easier. I know there's "end" timestamp posted to the ajax, so I know the devs will be able to fix this easier...
Hope this helps somebody...