And even then, when the law will have to change to address the Supreme Court rulings, the FBI will probably still push to basically ignore some of the Supreme Court decisions, already knowing they are unconstitutional. But if that can buy them an extra 5 years of abuses before the NSLs reach the Supreme Court again and the law has to change again, they are more than happy to play that cat and mouse game.
The GCHQ in the UK has been doing the same thing. By the time the previous surveillance law is declared illegal, they will have already passed a new surveillance law that would have to be challenged in court again, and on and on we go.
They did it when the data retention law was declared invalid by the CJEU and they made the Parliament quickly pass DRIPA in 2014 to "make it all legal again". And now the CJEU said DRIPA was invalid as well. But they had already passed the Investigatory Powers Act, which will likely have to be brought in court itself, too, to be made invalid.
By then they'll just pass an "amendment" to "make it legal again", even though it likely won't, because none of the mass surveillance "features" they want in these laws will ever be considered legal either by the CJEU or by the European Court of Human Rights. But they are also happy to play the cat and mouse game.
The EU also has the Charter of Fundamental Rights of the European Union. The final court for that is the European Court of Justice (or Court of Justice of the European Union) in Luxembourg. The ECJ is a EU organ, and appeals instance for violations of EU law in general. As such, since the ECHR is party of EU law by treaty, the ECJ also handles cases that involves the ECHR.
Once the UK leaves the EU, it will no longer be bound by judgements of the ECJ, but it will be bound by judgements of the ECHR.
The UK Human Rights Act sets out the obligations for the government with respect to the ECHR. The ECJ obligations I believe are indirect via the European Communities Act 1972, which gives EU law and treaties primacy over UK law.
Indirectly, leaving the EU does make it legally possible for the UK to withdraw from the ECHR, but that would still mean leaving the Council of Europe as well, but that's unlikely - it would put it in company with Kazakhstan, Belarus and the Vatican City as the only European states which are not CoE members (the Vatican is an observer).