The payments aren’t neraly 2 times as much, because there are 15 years less interest and often the rate on a 15 year loan is lower. Not as many 15 year loans default as 30 year. We refinanced a home from a 30 year to 15 year fixed. THe interest rate had come down a bit since the original mortgage was issued. The 15 year in that case ended up costing us about 16% per month more than the 30 year. But it all depends on the rate the 30 year mortgage caries, and what you can get on a new 15 year. It is definitely worth looking into with rates as low as they are now.
BTW, @tedibear gets close to the same thing with far less risk of overreaching. Think the equation through to fit your situation.