There are a lot of people analyzing the legality of the President's actions in authorizing eavesdropping without a search warrant on international calls (calls between the U.S. and other countries) where a party to the conversation has some connection to terrorism. One analysis was linked to at several popular sites: Jonathan Adler in the Corner, Belmont Club and Powerline Blog. The conclusion of the analysis is that the President's actions were constitutional but illegal.
The point (I think) was that the President acted within his constitutional power as the Commander-in-Chief but likely violated one or more laws passed by Congress that would appear to require a search warrant. I agree with the conclusion that the President's actions were constitutional. I disagree with the conclusion that his actions were illegal for the very reason that they were constitutional.
Essentially, I think the analysis linked to is much more complex than it needs to be. The basic flaw is that the analysis appears to assume that Congress, by enacting a law, could extinguish some of the powers of the President as Commander in Chief. It cannot, and any law that would purport to is unconstitutional to that extent.
Therefore, once it is determined that the President is acting within his constitutional powers as Commander-in-Chief, there is no need to analyze any further. No law passed by Congress can impede him in that capacity. To find otherwise would allow congress to take away the President's constitutional powers and duties, a clear threat to the separation of powers.
In other words, in this case, if his actions were constitutional they were also legal.
On the constitutionality issue
In the end, it is up to the Supreme Court whether the President’s actions were constitutional (although the President is also vested with power to interpret the Constitution). However, Congress has passed a law essentially authorizing the President to wage war on Al Qaeda and affiliated terrorist groups. As the Commander-in-Chief, the President has broad power to prosecute the war. The Fourth Amendment (no unreasonable searches and seizures and requirement for warrant) still binds the President acting as Commander-in-Chief. However the Constitution is not a suicide pact. The President has the power to do what is necessary to defend it and the courts are deferential to his judgment about what is necessary. So, in the end, the scope of what is considered a reasonable search and seizure is broadened in the national security context and the requirement for a warrant seems not to exist. Examples of the deference the courts have given a President in a time of war include: (1) Lincoln's suspension of Habeas Corpus for citizens (the right to be brought before a court so it can be determined whether or not that person is imprisoned lawfully and whether or not he should be released from custody) during the civil war; and (2) the detention of Americans of Japanese descent during WWII. I do not see how the U.S. Supreme Court could go from allowing those activities to denying the current President the very limited power to intercept conversations to and from telephone numbers that are found in laptop computers of captured suspects of an organization that has expressly vowed to kill as many Americans as it can.
I think that once again we are seeing the Democrats (and weak-kneed Republicans) attempt to frame the issue in terms of law enforcement. There is a good reason (from their perspective) to do this. It appears to give them control over his actions. In the law enforcement context, the President is simply acting as the chief executive where he is more subservient to the Congress. They enact the laws and he must execute them. Generally, he can only do what their laws allow him to do - which is exactly what the Democrats want. On the other hand, when he is acting as Commander-in-Chief and we are at war he is not subservient to Congress.
The tactic of treating this like a criminal search matter is compelling to the Public. The public is used to the President acting in his more subservient role as chief executive. They are also familiar with television and movies which show the police obtaining warrants before they conduct a criminal search. They think that they are always required. It will be somewhat difficult to explain to the public that a warrant may not be required to conduct a search in the national security context. The Democrats are counting on the public having a hard time adjusting.