First of all, asteroids aren't readily available in low earth orbit. You have to go further than that to get one - a lot further. The Dawn mission arrives in orbit of Vesta, located in the asteroid field between Mars and Jupiter, tomorrow. It was launched in 2006 and the mission wasn't exactly cheap - and those were just the costs of sending a small probe over there, not something that would bring with it enough power to lug an asteroid back towards Earth. Anyway, in order to get an asteroid mined out in Earth orbit, you'd have to satisfy several criteria.
First, you'd need to know the exact size, composition, mass, and location of your target asteroid. You can't exactly send back Pallas or Ceres, those are way too massive, and right now we lack most of the data on smaller rocks present that would make such a mission feasible (hell, we lack most of the data on the larger rocks, which is why Dawn is out there on final approach to Vesta right now). This means years of sending probes to map out suitable asteroids - Dawn will just study Vesta and Ceres.
Then, you'd need to transport over an incredible amount of whatever it is you plan to use to get your target asteroid out of it's trajectory and on course for Earth. This would involve years of R&D and transporting costly material first into Earth orbit and then towards your target asteroid. Then you'd need to somehow remotely attach whatever it is you're using to propel the asteroid towards Earth - an array of boosters, a large explosive device, whatever. You'd also need to be very accurate or you may very well end up being responsible for wiping out every living thing on Earth. No pressure. Thousands of billions of dollars later, your most expensive space project to date (hell, most expensive project in the history of mankind, period) has produced a giant rock in orbit of Earth you can now mine at a hefty price (since it's still expensive as all hell to transport stuff up and down from just low Earth orbit - and you wouldn't park such an object in LEO due in no small part to extreme risks involved - you'd park it further out exponentially increasing the costs of reaching it). That rock better be made of Unobtanium laced with the purest processed heroin to justify the costs and risks.
Just wishing for a more elaborate space program isn't going to make it feasible. Fact of the matter is, while we have the technology to "get there", barely, we don't have the technology to actually do anything with it while making it cost effective and at least moderately safe. We're simply not there yet in terms of technological advancement.