Firstly, your code is buggy. You take a `day` argument, but you never use it for anything. You always return mondays.

But worse, you're incrementing dates like so:

    new Date(today.getFullYear(), today.getMonth(), today.getDay()+x);

Spot the error? You're passing `getDay()+x` as the _date_ argument. But `getDay()` returns the weekday number (0-6) - not the day-in-month.

So today, Thursday the 5th of November 2015<sup>1</sup>, you're in effect saying:

    new Date(2015, 10, 4 + x);

The year's correct, and the month's correct (January is zero), but the date is 1 day off. Thursday is day #4 in the 0-6 weekday scheme - but really, today's the _5th_ of November.

So if you were to run this on the, say, the 30th of November, you'd actually be using the 1st of November as your start date, since the 30th's a Monday.

I also have to wonder why you've created a function, which builds an array just to hold a list of numbers, which you _then_ `map` to dates. The simpler way looping through incrementing numbers is a plain old `for`-loop.

Anyway, while calendars are complex, there's one thing that thankfully doesn't change: There are 7 days in a week. So you're creating 7 times more dates than you need, and filtering most of them away. You could consider simply skipping 7 dates at a time from the first occurrence.

Thirdly, don't mix calendar dates and raw time calculations like your division by milliseconds in a day. Switching back and forth between daylight savings time can cause all sorts of nonsense when mixing time and date. Some calendar days are 25 hours long, some are 23.

Anyway, there are two ways you can go. Either find the first occurrence of the day you're looking for, and then repeatedly add 7 days until the year rolls over; or add 1 day at a time until the year rolls over, storing those days that match what you're looking for.

This is the latter, since it's shorter:

    function remainingDays(weekday) {
      var current = new Date,
          year = current.getFullYear(),
          dates = [];
      
      // a simple helper function
      function nextDay(date) {
        return new Date(date.getFullYear(), date.getMonth(), date.getDate() + 1);
      }
    
      // as long we're in the same year, keep adding 1 day,
      // and store the ones that match the wday we're looking for
      while(current.getFullYear() === year) {
        if(current.getDay() === weekday) {
          dates.push(current);
        }
        current = nextDay(current);
      }
      
      return dates;
    }

No need to build ranges, map, and filter them. Just a `while` loop and `push`.

<sup>1) Happy Guy Fawkes day everyone</sup>