If a Big Player decided to undermine bitcoins then they could do so very easily. All they'd have to do is throw enough resources at it to capture the majority of the mining capability and they'd be able to sit on whatever they mine. This would be likely to temporarily push up the value of existing coins, thereby making it much more difficult for any new adopters to jump in.
If the value of existing coins goes up, then people don't need as many of them. So it doesn't matter that they're more difficult to get. It cancels out.
Then when the number of people using bitcoins contracts and the number of services accepting them in payment shrinks (both of which I think would be likely in this scenario) the value of each coin would decrease as the existing supply outpaced the demand.
Then, when the value drops, people can get as many bitcoins as they need. So if you assume the problem occurs, it will solve itself. This tends to suggest the problem won't actually happen.
If they push up the price of bitcoins, people will need fewer of them. If they make bitcoins expensive and thereby discourage people, the reduced demand will lower the price, ending the discouragement.
And don't forget the 51% thing. That's potentially a very big issue. If someone could control the block chain, even partialy, then the intergity of the entire system would be compromised.
That's true, but that's a different issue from them mining. At worst, they could significantly increase the time it would take before you could be assured a bitcoin transaction wasn't going to be reversed.