The FISA courts were set up during the Cold War era, when there was no immediate threat of attack upon the U.S., and there was the general opinion that any such attacks would be preceded by sufficient warning signs that the need for an "instant warrant" to record a conversation, which would be used in a court case of some sort, was not deemed necessary. The U.S. is now in a state of war, albeit against an extra-national para-military organization instead of a recognized, geographically based government.
Let me pose the problem: We have a recognized leader of such an extra- national group, which has publically declared "war" against the U. S. using (among other methods) terror attacks against civilian targets -- let's call him Jafar al-Vizier -- who is currently residing in a foreign country, say, the Sultanate of Agrabah. The NSA is monitoring, legally, all of his conversations -- landline, wireless, satellite, Internet, etc. One day, al-Vizier makes a phone call from Agrabah to a previously unknown associate -- let's call him Iago Parrot -- who is located in the U. S. Under your "no wiretaps without a court order" view of the world, the NSA would have to immediately stop monitoring the call, and initiate proceedings for a FISA warrant, which will take days to obtain, if not weeks.
Now the call from al-Vizier to Parrot may have been perfectly innocent ("hi, how's the kids, etc.") -- or it could have been a triggering call to a "sleeper" cell to initiate an attack plan on a U. S. target, potentially killing or injuring hundreds or thousands. In either situation, since the conversation may have lasted only a few minutes, and it's likely that al-Vizier may never call Parrot again, the opportunity to determine the nature of the call is lost, and the need for a wiretap warrant is moot.
However, since this is a MILITARY situation, not a civil one, this isn't a 4th Amendment "unreasonable search and seizure" sitation, but an Article II, section 2 situation, with the President acting as commander in chief of the military, authorizing a military operation to prevent an attack on the country. In that capacity, the NSA *can* continue to monitor al-Vizier's call to Parrot, and, if it's determined to be of no military value, discard the recordings, or, if it IS of military value, pass the information to the appropriate military commanders and/or domestic defense organizations (FBI, local law enforcement, etc.) to take the appropriate defensive actions. There is no intent to use the information gathered for legal proceedings, only to guide military operations.
While I've posed what seems like a hypothetical, it's not. It's actually happened at least twice. Once since 9/11 (the Brooklyn Bridge bomb plot), and once during WW II (foiling a German commando raid on the East coast). In either case, I doubt that the vast majority of Americans would consider the monitoring of the conversations of persons intent on attacking the U. S., whether they happen to be inside or outside of the country, to be "unreasonable".
And there is historical precedence for the U. S. engaging in military action against an extra-national para-military organization: The Barbary "pirates", during the years 1801-1815.
As a side note, it is the 1796 treaty with these "pirates" that supposedly contains the phrase "the government of the United States of America is not in any sense founded on the Christian Religion", which is often used to justify all manner of elimination of religion from the public sphere. In fact, that phrase does not appear in the original Arabic version of the treaty, but was inserted in a translation by Joel Barlow, the U. S. Consul General at Algiers. A discussion of the problems with the Barlow transalation is available from the Avalon Project of the Yale Law School, at