setTimeout fires immediately if the delay more than 2147483648 milliseconds

Since you are limited to 32 bits, just wrap setTimeout in a recursive function like so:

function setLongTimeout(callback, timeout_ms)
{

 //if we have to wait more than max time, need to recursively call this function again
 if(timeout_ms > 2147483647)
 {    //now wait until the max wait time passes then call this function again with
      //requested wait - max wait we just did, make sure and pass callback
      setTimeout(function(){ setLongTimeout(callback, (timeout_ms - 2147483647)); },
          2147483647);
 }
 else  //if we are asking to wait less than max, finally just do regular seTimeout and call callback
 {     setTimeout(callback, timeout_ms);     }
}

This isn't too complicated and should be extensible up to the limit of javascript number which is 1.7976931348623157E+10308, which by that number of milliseconds, we will all be dead and gone.

The upper limit of setTimeout is 0x7FFFFFFF (or 2147483647 in decimal)

This is because setTimeout uses a 32bit integer to store its delay value, so anything above that will cause the problem

If you want a timeout which fires after an X ammount of days, you could try to use setInterval instead with a lower delay value like this

function setDaysTimeout(callback,days) {
    // 86400 seconds in a day
    var msInDay = 86400*1000; 

    var dayCount = 0;
    var timer = setInterval(function() {
        dayCount++;  // a day has passed

        if(dayCount == days) {
           clearInterval(timer);
           callback.apply(this,[]);
        }
    },msInDay);
}

You would then use it like this

setDaysTimeout(function() {
     console.log('Four days gone');
},4); // fire after 4 days