Iterate through series of timers
If you only need the entries once, you could simply keep using shift until there are no more entries:

var exercises = [
    {
        "desc":       "Pushup/Pullup",
        "countdown":  30
    }, {
        "desc":       "Squat punch",
        "countdown":  45
    }, {
        "desc":       "Jumping jacks",
        "countdown":  60
    }
];

function exerciseTimer(exercises) {
    // do stuff
    var exercise = exercises.shift(),
        tt = setInterval(function() {
            // write html to the page
            exercise.countdown = exercise.countdown - 1;
            //Does it work ?
            console.log( exercise );
            if (exercise.countdown &lt;= 0) { 
                exercise = exercises.shift(); 
                if(!exercise) {
                    clearInterval(tt);
                }
            }
        }, 100);
    };

exerciseTimer( exercises );


I would also suggest to not make the type of the variable part of the variable name. exercise and exercises are much easier to read than exerciseArray and exerciseObject.