Throughout US history, a warrant has been the only Constitutional requirement (4th Amendment) to search the property of a suspected criminal. That is not at issue with the request to unlock the San Bernardino terrorist's iPhone, since the FBI presented a warrant to Apple. The issue completely stems from the cryptographic technology used in iOS devices over the past few years.
After the NSA spying came to light, there was so much pushback from customers of tech companies for their backdoors that many of the companies beefed up security on their devices. Apple in particular employed point-to-point encryption for iMessage, prevented app developers from tracking any more than the GUID of that particular installation of the app (rather than fixed values, like the MAC address), allowed device owners to reset ad tracking IDs and the Siri session ID, and, most notably, moved all encryption for the device into a section of the CPU called the Secure Enclave. Every modern iOS device keeps contents fully encrypted in the device's storage. The decryption can only be achieved with a combination of the Secure Enclave's decryption key and the password. (TouchID inserts itself into this decryption chain, unless 48 hours have passed, the device has been restarted, or the TouchID hardware has been compromised.)
So, with all this said, Apple has no backdoors to the encryption because the password is needed to finalize the decryption process. The FBI can brute-force the password, but iOS devices can be set to either wipe all contents or temporarily lock the device after a certain number of bad login attempts. Presumably, the terrorist set up such security and has a strong enough password that the FBI is at a loss on how to proceed with the decryption.
On the simplest level, the FBI want Apple to assist in overcoming the lock-out feature so that they can brute-force entry into that iPhone (which can take a very long time, if a strong password was used). This would involve changing the settings on the device, but those settings cannot be changed without decrypting the device first.
On a more complex level, the FBI would like an easier way to access the iPhone, via a backdoor in iOS on just that device. This backdoor is where Tim Cook at Apple has been giving the most pushback because that would open a Pandora's box to any third parties potentially hacking an iOS device. This would require moving the encryption from the Secure Enclave into a software solution. Such a move severally cripples the security for everyone iPhone on that version of iOS and newer. This is the reason for the pushback, not the Constitutionally valid request from the FBI for data extraction of a terrorist's iPhone.
I'd like to hear everyone's thoughts on this situation.