You're right, what they are using has the ability for time, so either it really is coming out at midnight, or whomever coded the site didn't bother picking a time:
var AnticipateDay = new Date();
AnticipateDay = new Date('03/01/2012 00:00');
jQuery('#anticipate-timer').countdown({until: AnticipateDay,layout: '<span class="timer"><strong>{dn}</strong> {dl}</span><span class="timer"><strong>{hn}</strong> {hl}</span><span class="timer"><strong>{mn}</strong> {ml}</span><span class="timer"><strong>{sn}</strong> {sl}</span>'});