The entire continent of Antarctica comprises 14,000,000 km squared, or 1.4x107 km2. The area of the earth's salt water (all seas, oceans, bays, and so forth, taken together) is approximately 3.8x108km2 (numbers are from Wikipedia and so not authoritative, but probably in the ballpark).
So to keep my units the same I converted 49 feet to meters (it's 14.935m) and then to kilometers (1.4935x10-2 km). I then figured out the volume required to add this number to the world's sea levels (assuming the boundaries of the salt water remain the same, which is intensely conservative) and arrived at:
3.6x108km2 x 1.4935x10-2 km = 5.3766x106 km3.
...that is to say, 5.3 million cubic kilometers.
If we were to assume, then, that this much water were evenly distributed over the area of ALL of Antarctica, then the height of it would be 5.3766x106 km3 divided by 1.4x107 km2 (the area of Antarctica), or 0.384 km, or 384 meters.
So the ice all over Antarctica would have to be four football fields deep, and all of it would have to melt in order to do what they say.
These numbers are not out of reason. The premise may be false, but the numbers are reasonable given the premise.
How many yards of dirt do I need to fill my 8ft square garden 15 inches deep?