It is often repeated that embassies are foreign territory. This is a mistake, and they are not.
By the concession of the host country embassies and consulates are under a foreign jurisdiction under international law. They are within the host territory, and their diplomatical status is given and can be taken away at will (though it is not very polite to go around revoking embassies).
They may be treated as foreign territory under the US legal domestic regime (like federal buildings are treated as having their own jurisdiction), but they are surely not a foreign dot in the map. So I imagine the Constitution should take precedence over whatever other domestic policy pretending embassies are not US soil for spying purposes. Though I guess spying on foreigners would be okay anywhere anyway.