This attachment does not have to come with the machine. You just need to have a machine with the correct type of shank (low shank) and a centered needle.
Here is a link to the attachment on Amazon ($10):
http://www.amazon.com/Side-Cutter-Se.../dp/B001HFBBA0
Be sure to read all of the information on Amazon, including questions asked and answered:
http://www.amazon.com/forum//ref=ask...A0&cdSort=best
and user reviews:
http://www.amazon.com/Side-Cutter-Se...ustomerReviews
Edit: I would not want a Singer sewing machine. This is a company that has had a bad rep for the last 20 years or so. The last thing you want in a sewing machine that does decorative stitches is a machine that does not hold its tension well! Brother machines currently have a much better reputation than Singer machines.
Edit 2: The above attachment is not the only one available. Here are links to others sold on Amazon:
http://www.amazon.com/Kalevel-Multi-...dp/B00MPBF27I/
http://www.amazon.com/SINGER-Attachm...dp/B00G6TW7ZK/
Also, I just want to point out that this attachment does not do many things that a serger can do. For example, you can still easily stretch knit fabric edges. A serger will have "differential feed" which moves the knit fabric without stretching it -- something a sewing machine cannot do.