The primary problem is indicated in the previous post.  The depth of the sunken rig is very difficult to control in terms of being able to place any item on it to stop or contain the flow.  The deeper an objects goes, the greater the chance ice develops on it or other complications arise. Prior oil spill containment have not had to take place so deep within the body of water.  The other problem is that the rig did not feature an automatic shutdown valve so that when it exploded, the oil continued to spill out at an enormous rate.  The oil rig pumps and drills at such a high rate of velocity and magnitude that stopping it is a very arduous task.  Trying to contain a spill that renders out close to 20,000 gallons of crude oil a day is an extremely difficult task.

The above posts are certainly accurate, and let's also remember that the technology for stopping such a spill not only exists but it was installed on the Deepwater Horizon drilling rig - it simply wasn't maintained and once the leak/explosion had happened, it became much more difficult to stop.

Drilling at such depths is complicated and time consuming, not to mention expensive.  So they are drilling relief well to take off some of the pressure of the leak so it can be capped, but that takes a long time to do, and the relief well has to tap directly into the original drilling shaft, which is only a few feet across.  It's like hitting a needle in a haystack in a field of haystacks.  The relief wells are the best option at this point, but they are by no means guaranteed to work.

The main reason that the oil spill is such a difficult thing to deal with is the fact that it is so far under the surface of the ocean.  At those depths, the water is so cold and the pressure so intense that things that would work nearer to the surface are much less likely to work.

A great example of this can be seen in what happened the first time that they tried to lower the dome to catch the oil that was coming out of the well.  They got the dome in place, but the cold and the pressure did things to gasses that were leaking out along with the oil that made it impossible to use the dome in the way that it was meant to be used.