If there was a communication protocol that encrypts at the very low-level, this would solve the problem of wiretapping entirely and for all.
There is: IPSec
The answer you are looking for is Bitmessage, or something that works like that.
End-to-end encryption is not a solution
There is metadata to think of. Take the Dutch system for wiretapping: it's illegal without a warrant. But the police is allowed to see, without warrant, your address and name, your phone number, whom you're calling, when you called, your approximate location (based on cell towers I assume), and when the call ended. That's a lot of information. I'm assuming that's why you're looking for such low-level encryption: the IP headers also get encrypted and it's not possible to find out whom you're communicating with.
Unfortunately, that's the way the internet works. If intermediaries, including your ISP and thus the police, can't tell where a packet is supposed to go, it won't get there. You'd have to setup a mesh network where everyone talks to everyone, and only the peer that has the decryption key can decipher your message.
... which is exactly what Bitmessage does ;)
But let's explore your low-level encryption idea a little bit further.
How'd you setup end-to-end encryption anyway?
Skype promised end-to-end encryption. They did that for a good while I hear, but nowadays it's possible to wiretap it. How would you do that? First we have to know how the end-to-end encryption works.
Your goal is to exchange private information over an insecure channel (i.e. the internet) between a number of parties (you and all your contacts). In order to do this we need to meet in person and exchange encryption keys... but one of your contacts is in Australia and you're in Europe... so we need something better.
Someone came up with asymmetric encryption: You generate a public and private key, and only share the public key with the world. Then anyone can encrypt a message (using the public key) while only you can decrypt it (using the private key). You can't decrypt the message using the public key (at least, not in the scheme we're currently using; signing data is a different story and different concept).
Now we have a big problem: How do I send someone my public key, and can that person prove that I was the one that sent it?
Here we are. This is why end-to-end encryption is a lie. Skype can give you any key you want, they can read the contents, then re-encrypt it using the correct public key, and send it to your contact. Wiretap complete.
So how is Bitmessage any better?
Well to tell the truth, it's not that much better than plain old asymmetric encryption. But once you have succesfully exchanged the keys out of band, both the message contents and the metadata are secure. It's still possible to see that you're sending a Bitmessage message and how large it is, but not whom the sender and receiver are.
Okay and why aren't we all using it yet?
If mesh networks worked so well, we would all be using it. The problem is that it's incredibly easy to flood the network, but even without trying the network would be completely flooded if all our https traffic was switched over to bitmessage traffic. Bitmessage 'solves' this by requiring a certain amount of work before being allowed to send a message (the larger the message, the more work it requires), but it's not really ideal for huge-scale systems.
Tor is an alright alternative. The issue is that if you own a great number of nodes, you have a reasonable chance of decrypting some traffic. It's now known that the NSA is very interested in Tor and also owns a great number of nodes.
Overall, there is no ultimate solution, and any good security researcher will tell you the same. There are different systems which all have advantages and disadvantages. Some may work better in one case while others work better in other cases.
The best alternative will be quantum locking of communications in peer to peer sessions but it is still developing, extremely expensive, has distance limitations for now