javascript: pause setTimeout();

You could wrap window.setTimeout like this, which I think is similar to what you were suggesting in the question:

var Timer = function(callback, delay) {
    var timerId, start, remaining = delay;

    this.pause = function() {
        window.clearTimeout(timerId);
        timerId = null;
        remaining -= Date.now() - start;
    };

    this.resume = function() {
        if (timerId) {
            return;
        }

        start = Date.now();
        timerId = window.setTimeout(callback, remaining);
    };

    this.resume();
};

var timer = new Timer(function() {
    alert("Done!");
}, 1000);

timer.pause();
// Do some stuff...
timer.resume();

Something like this should do the trick.

function Timer(fn, countdown) {
    var ident, complete = false;

    function _time_diff(date1, date2) {
        return date2 ? date2 - date1 : new Date().getTime() - date1;
    }

    function cancel() {
        clearTimeout(ident);
    }

    function pause() {
        clearTimeout(ident);
        total_time_run = _time_diff(start_time);
        complete = total_time_run >= countdown;
    }

    function resume() {
        ident = complete ? -1 : setTimeout(fn, countdown - total_time_run);
    }

    var start_time = new Date().getTime();
    ident = setTimeout(fn, countdown);

    return { cancel: cancel, pause: pause, resume: resume };
}

No. You'll need cancel it (clearTimeout), measure the time since you started it and restart it with the new time.

A slightly modified version of Tim Downs answer. However, since Tim rolled back my edit, I've to answer this myself. My solution makes it possible to use extra arguments as third (3, 4, 5...) parameter and to clear the timer:

function Timer(callback, delay) {
    var args = arguments,
        self = this,
        timer, start;

    this.clear = function () {
        clearTimeout(timer);
    };

    this.pause = function () {
        this.clear();
        delay -= new Date() - start;
    };

    this.resume = function () {
        start = new Date();
        timer = setTimeout(function () {
            callback.apply(self, Array.prototype.slice.call(args, 2, args.length));
        }, delay);
    };

    this.resume();
}

As Tim mentioned, extra parameters are not available in IE lt 9, however I worked a bit around so that it will work in oldIE's too.

Usage: new Timer(Function, Number, arg1, arg2, arg3...)

function callback(foo, bar) {
    console.log(foo); // "foo"
    console.log(bar); // "bar"
}

var timer = new Timer(callback, 1000, "foo", "bar");

timer.pause();
document.onclick = timer.resume;