When the arc reactor was removed from Tony's chest in the first movie, he was hardly able to move and barely made it to his lab. I thought it was just powering the electromagnet to keep the metal from hitting his heart. How did removing it make him seem like he can barely move? Did it end up supplying him with extra strength that he just became used to?
At one point in the first movie, Tony removes his Arc Reactor to upgrade it, and in doing so remarks to Ms. Potts that he is going into cardiac arrest. "Oh, nothing, I'm just going into cardiac arrest, because you..". He is trying to display the same symptoms of a cardiac arrest patient. Poorly might I add. I believe his monitor read V-Fib (which means he is going into cardiac arrest -- it's basically an irregular heartbeat). Cardiac arrest and a heart attack are very different. A Heart attack (or Myocardial Infarction) patient is able to move around and do things, with a vice like pain in their chest and difficulty breathing like he displayed (so he displayed heart attack NOT cardiac arrest).
So why you might ask? If removing it truly induced heart attack so quickly, then that is your answer. It could also have something to do with the device that Obadiah Stane used to paralyze him...
I just watched this squence on the DVD.
Tony had just been paralyzed by the sonic weapon used by Obadiah Stane - he didn't become weak because the Arc reactor was removed, he was weak because he was still trying to shake off the effects of the paralysis.
Here's a screencap of the scene - you can see the weapon in Obadiah's hand, and the ear protection in his ears:
The injury was not just a single piece of sharpnel. The device was designed to keep all the remaining pieces that were not able to be surgically removed from moving further into the heart cavity. I would consider the pain the equivalent of having a heart attack and cardiac pain has been described as excruciating often accompanied with weakness.
Heart attack symptoms vary widely. For instance, you may have only minor chest discomfort while someone else has excruciating pain. One thing applies to everyone, though: If you suspect you're having a heart attack, call for emergency medical help immediately.