SHA-256 Reversing A String of Equal Length I've done a lot of reading on how SHA-256, I've found that SHA-256 is irreversible because more data is fed into the hashed string than the hash string contains.  But, what if the data that was inputted was equal in size to the output string, a string of 64 characters is inputted a string of 64 characters is outputted.  Would it be possible to reverse the hashed data back to the original string?
SHA256 gives 256 bits, which is 32 bytes, not 64 "characters" (please use the well-defined bits and bytes). When written in hexadecimal notation, you need 64 characters from 0-9a-f, but the length of the hash is 256 bits. 

Yes, you could invert the hash. Unfortunately, a straightforward lookup table would be too large to store, but you can still do brute force without memory. This would take you on average $2^{255}$ tries (that's many). 

There have been papers, like "Bicliques for Preimages: Attacks on Skein-512 and the SHA-2 family" which discuss preimage resistance attacks on the SHA-2 family, but they're, as far as I know, all academical breaks (meaning they cannot really be exploited efficiently.