You need one or more threads. Real GUIs I have experience have a single UI thread that runs in the background to handle these sorts of things.

Can't you just use Allegro 5's timers to keep track of time? From there, it's just a matter of getting the difference in time to whatever classes manage the timed events. I don't think that it makes sense to have a createTimedEvent method on TextBox, mind you.

But al_rest would sleep the thread, and while difference seems like a good idea, it feels messy to me as a solution.

I'd just register a timer, and call your function when you get the timer event. And if you want it to only fire once, just stop the timer before you handle it.

You can do the same thing without the extra thread. Setup the timer each time to fire off the next time any timer is due, and call all timer handlers due at that time. But thats really just an extension of my suggestion.

I do this in my game with things like switching game states. For example I have a bunch of UI stuff, and I want them to play a "close" animation before switching the game state, which means I need to either a) send an event when the animations are finished playing, or b) just wait a certain amount of time. I chose B.

I have a global in my program that is set with al_current_time() at the beginning of every frame. Objects then store "time to do X action" values that compare themselves with the current time.

float time = al_current_time();

float time_to_do_something = time + 5.0f; // do something in 5 seconds

while ( blah )
{
    time = al_current_time();

    if ( time >= time_to_do_something )
    {
        DoSomething();
    }
}

To achieve your example I would probably create a class containing a "time to do action" variable, a function pointer/functor, and some data to pass. On calling createTimedEvent() I would new one of these classes and it add it to a list that the class is keeping track of.

The following is all pseudo-code, but createTimedEvent() might look something like this:

void MyClass::createTimedEvent( function *func, void *data, float delay )
{
    TimedEvent e = new TimedEvent( func, data, delay );
    timedEventList.push_back( e );
}

Then you'd check your list every frame.

I would have thought that you could just run a single timer at the lowest reasonable rate and work around the frame rate, draw rate, and timed events based on that.

Don't be so scared of creating new threads. If it works out best to handle the animations in the background, then do it. Creating new threads is essentially free.