jQuery Answer
You will have to setup the starting date for it to increase daily. The idea is to get the date difference and add it to that counter.
HTML
<p class="counter-number">843</p>
jQuery
jQuery(function() {
    // Get Starting Number
    var starting_number = parseInt(jQuery('.counter-number').text());
    // Create Day difference (because it increases by 1 each day)
    var preset_start_date = new Date("21/03/2015");
    var current_date = new Date();
    var timeDiff = Math.abs(current_date.getTime() - preset_start_date.getTime());
    var diffDays = Math.ceil(timeDiff / (1000 * 3600 * 24)); 
    var final_counter = starting_number + diffDays;
    jQuery('.counter-number').text(final_counter);
});
I haven't tested it. But  this is an idea to get that done.