There is much concern, particularly among Republicans, about the use of drones as a weapon of war. Even Democrats wonder about the lack of judicial review in cases where the president or anyone else orders a drone strike on a military target overseas. According to The New York Times, the president himself has said that counter-terrorism efforts should "be more transparent and fully consistent with checks and balances."
The current version of checks and balances is the Foreign Intelligence Surveillance Court, which went into effect in 1978 and governed the use of wiretaps as a method of gathering intelligence. Under the act, if the president, the National Security Agency or the FBI want to tap your phone, the FISA court must approve it.
The FISA law was in full effect when George W. Bush took office, but even then, the government was able to hear almost everything Americans said and most of what people around the world were saying to each other. Many, if not all, of these wiretaps were approved by FISA, and very few were turned down. The Times reported that from 1979 to 2011 only 11 of 32,000 wiretap applications were rejected. The Times suggests that FISA's "presence has helped ensure that the administration's requests are serious."
I suggest, based on the above numbers, that FISA is a fig leaf used to cover the almost absolute power of the United States government to listen in on any conversation it wants to. It may be possible to invent another fig leaf that would have the power to reject drone strikes, but I can't imagine that the new court would be any more than a fig leaf. If the President of the United States or the DOD or the FBI says this country is at risk from the actions of its enemies, I cannot imagine that any court could say no because if the court rules wrongly, it will be blamed for the deaths that ensue.
If in the end it makes Americans, Republicans and Democrats, happy to find another fig leaf to make us all feel more virtuous, so be it. But based on FISA's record, it's not going to make any difference, after all, a fig leaf is still a fig leaf.