Including wp-blog-header.php from functions.php remote call?

You shouldn’t need to make direct calls to your theme files – use the AJAX API, and make all requests to admin-ajax.php (that way, WordPress’ll be loaded for you, and you won’t need to assume the file hierarchy in order to load it manually).

$.get(
    '<?php echo admin_url( 'admin-ajax.php' ) ?>',

    {
        "color_theme" : "test",
        "color_spot" : "1",
        "action" : "change_color"
    },

    function( data ) {
        doColor( '#theme_header_color', data );
    }
);

And in functions.php;

function __do_color_ajax()
{
    $theme = $_GET['color_theme'];
    $spot = $_GET['color_spot'];

    // do something

    die( 'AJAX output' );
}
add_action( 'wp_ajax_nopriv_change_color', '__do_color_ajax' );

See how the suffix of the hook, wp_ajax_nopriv_change_color, matches the action variable in the AJAX request? See this SE answer for more info.

Note I’ve also prefixed the other AJAX request variables, as you should namespace custom $_GET and $_POST variables in the same way you do PHP variables and functions.

Also check out the codex on the AJAX API.