What is being hashed in this function?  <-- let's call this item x

If the total number of possible x is smaller than 256bit space that sha256 provides than an attack would come in the form of a table of all sha256(x) values.

If all of the possible combination's of x is greater than the 256bit space, then here is some math for you (the attack would be at the hash value itself rather than a table on known sha256(x)):

What follows is from www.atmel.com/dyn/resources/prod_documents/doc8668.pdf

If there are 256 bits in the key, then after 2^255 attempts the attacker has a 50% chance of finding the right key and after 2^256 attempts he has tried all possible keys and is guaranteed to have found the key.

Here are some estimates of big numbers:

2^66 Number of grains of sand on the earth
2^76 Number of stars in the universe
2^79 Avogadro's number. The number of carbon atoms in 12 grams of coal.
2^96 Number of atoms in a cubic meter of water
2^190 Number of atoms in the sun
2^255 Number of attempts to find the key value from above

But what about very well funded entities such as the US National Security Agency (NSA)? Could they build a machine to crack a 256 bit key? Assume they could build a theoretical nanocomputer that executes 10^13 instructions per second (approximate rate of atomic vibrations) in a space of a cube with a side that is 5.43nm across (This is the approximate size of a silicon lattice10 atoms wide, or a crystal containing 1000 silicon atoms). Assume that it could calculate an attempt in 10 cycles. Such a computer the size of the earth would take more than 10^13 years (roughly 58 times the estimated age of the earth) to attack a 256 bit algorithm via brute force.