Create a pop-up class
Most of your code looks good
The one improvement is do not overwrite the initial settings, instead extend from defaults and the options provided. Use $.extend for this

 popup.settings = $.extend(defaults, options);


Also store the reference of this into a variable so that it will be used inside event handlers and anonymous callbacks.

var Popup = function() {
    var popup = this,
        new_id = "div" + Date.now(),
        defaults = {
            id: new_id,
            container: "body",
            height: 200,
            width: 200,
            text: "&lt;div&gt; created with \"id\" = " + new_id,
            x: 100,
            y: 100,
            position: "absolute",
            bgcolor: "red"
        };

    popup.create = function(options) {
        popup.settings = $.extend(defaults, options);
        var html = "&lt;div id=\"" +
            popup.settings.id + "\"&gt;" +
            popup.settings.text +
            "&lt;/div&gt;";
        $(popup.settings.container).append(html);
        popup.update();
    };

    popup.update = function(options) {
        popup.settings = $.extend(defaults, options);
        $("#" + popup.settings.id).css({
            "height": popup.settings.height + "px",
            "width": popup.settings.width + "px",
            "position": popup.settings.position,
            "top": popup.settings.y,
            "left": popup.settings.x,
            "background-color": popup.settings.bgcolor
        });
    };
};



var pop = new Popup(); // new popup is declared

pop.create({
    bgcolor: "green"
}); // popup appears green instead of read

pop.update({
    bgcolor: "blue"
}); // popup changes to blue