I wonder if the PRISM revelations might give defense attorneys a broad strategy to deal with inconvenient evidence: "the government was illegally intercepting my client's communications; they never would have found the {cocaine|bodies|plutonium} without these illegal intercepts, thus all evidence against my client flows from this tainted knowledge and he must go free."
That wouldn't work, because the defense has the burden of arguing that the evidence is tainted. Case law merely states that the tainted evidence will get excluded and that the defense must be given the opportunity to argue that the evidence is tainted.
Also, let's be clear, and stop saying "the government". Let's say "the NSA" is doing the wiretap. Then we can talk about "state prosecutors" or "federal prosecutors", and talk about how those prosecutors ended up with evidence obtained by tainted means.