I ran into a similar issue when building a custom pagination for a site I am working on.
The global variable I created in functions.php was defined and set to 0. I could output this value in my javascript no problem using the method @Karsten outlined above. The issue was with updating the global variable that I initially set to 0 inside the PHP file.
Here is my workaround (hacky? I know!) but after struggling for an hour on a tight deadline the following works:
Inside archive-episodes.php:
<script>
    // We define the variable and update it in a php
    // function defined in functions.php
    var totalPageCount; 
</script>
Inside functions.php
<?php
    $totalPageCount = WP_Query->max_num_pages; // In my testing scenario this number is 8.
    echo '<script>totalPageCount = $totalPageCount;</script>';
?>
To keep it simple, I was outputting the totalPageCount variable in an $ajax.success callback via alert.
$.ajax({
        url: ajaxurl,
        type: 'POST',
        data: {"action": "infinite_scroll", "page_no": pageNumber, "posts_per_page": numResults},
        beforeSend: function() {
            $(".ajaxLoading").show();
        },
        success: function(data) {
                            //alert("DONE LOADING EPISODES");
            $(".ajaxLoading").hide();
            var $container = $("#episode-container");
            if(firstRun) {
                $container.prepend(data);
                initMasonry($container);
                ieMasonryFix();
                initSearch();
            } else {
                var $newItems = $(data);
                $container.append( $newItems ).isotope( 'appended', $newItems );
            }
            firstRun = false;
            addHoverState();                            
            smartResize();
            alert(totalEpiPageCount); // THIS OUTPUTS THE CORRECT PAGE TOTAL
        }
Be it as it may, I hope this helps others! If anyone has a "less-hacky" version or best-practise example I'm all ears.