I have no problem with reasonable searches and neither does the Constitution.
We may debate as to what is 'reasonable', but I don't find monitoring foreign agents, especially in time of conflict, to be unreasonable.
True, but the devil is in the definition of "reasonable", or more precisely, in who decides what is "reasonable". If the searchers are the ones to decide which searches are "reasonable", then the fourth amendment is effectively nullified.
There is fairly good precedent for the interpretation of reasonableness in searches. For example, looking at what is in plain view is not considered an unreasonable search. This has even included cases in which a police helicopter hovered over a property observing what went on below, and this was (legitimately) upheld. Similarly, picking through someone's trash has been upheld, since one doesn't legitimately consider one's trash "private". The usual test is a "reasonable expectation of privacy".
There have also been some bad decisions. The "open fields" rule, which seems like a special case of "things in plain sight," has been extended to permit officers to trespass on private property without a warrant, to look at outdoor areas not visible from outside the property's boundary. This is clearly wrong, though it's currently legal. By contrast, it's both right and legal to conduct aerial surveillance, precisely because one does not own the airspace over one's property.
Historically, the interpretation has been that someone making a telephone call has a reasonable expectation of privacy. Thus, warrants are required for wiretaps.
The issue is confounded by the notion of "exigent circumstances", which essentially mean that some conditions can justify unreasonable searches. This reopens the original can of worms under a new heading, namely: who decides whether circumstances were exigent? If it's the searcher who decides, then the fourth amendment is again nullified.