Google currently allows copyright holders to request a takedown from the search giant's search results, but they only allow 10,000 URL requests per day, which just isn't enough for some copyright holders nowadays, and they're fighting with Google to raise the limit to 40,000 requests per day, which is supposedly enough for companies to request without reaching a cap.
Specifically, the Hollywood-funded anti-piracy organization BREIN and the RIAA, which both represent a handful of media companies, wants to increase the daily DMCA cap to 40,000, but wants to eventually remove the cap altogether at some point. Google has seen a huge spike in takedown requests recently, and it's large enough amount that Google is worried that it violates freedom of speech, but copyright holders say they are just looking out for their businesses.
However, it doesn't look like Google will budge on its set daily limit. The company says it can’t increase the limit because it may cause technical problems due to unexpected peaks in server performance. However, the RIAA isn't having none of that, and has said that Google has the resources to increase the limit. They also say that Google's number of allowed requests per day is "minuscule."
Copyright holders are afraid that if Google doesn't lift the limit of daily takedown requests, they fear that they will be unable to keep up with the numerous links (in the hundreds of thousands) that are added to Google search results every day. However, Google notes that BREIN is currently only sending under 5,000 takedown requests per day, far below the current 10,000 request limit. Then again, this certainly won't be the last that we hear from the RIAA and BREIN, so get out the popcorn and stay tuned.