I think the OPs question is more "given a set of transactions and a single timestamp, is it possible that all 64-bit nonce values could be exhausted without finding a hash that beats the difficulty?"
The nonce is actually only 32 bits, so the difficulty is the number of times you need to update the extra nonce.
In the coinbase there is a 100 byte nonce, so you have 2^832 options. However, some of those bytes have been assigned. The first few encode the distance from the block to the root, so the options is slightly reduced.
Every 4 billion hashes, you need to update the extra nonce, which requires rehashing the merkle tree from coinbase to root.