Traditional estimates of the mintage of the Proof 1856 Quarters run around 25 to 30 coins, which is the range we'ved used since the reboot of PCGS CoinFacts in 2008. However, as with any guess, there's a problem. PCGS alone has certified 28 Proof 1856 Quarter Dollars and, coincidentally, NGC has blessed the exact same amount (as of September 11, 2014). Even allowing for resubmissions, it is clear that traditional estimates are far too low. Companies such as Heritage have already noticed this disparity and ramped up the mintage to 100 Proofs in their January 2014 auction catalog description. Assuming the guesstimate of 100 Proofs is reasonable, it does not make the 1856 Quarter Dollar is a common coin in Proof. Remember that it has taken almost thirty years or third-party certification to get to this point and one can assume that the number of ungraded Proofs "out there" is small.
Looking at the current populations of the certified 1856 Quarter Dollar Proofs, it is clear that they are difficult to find nice. At PCGS, the most common grades are PR63 and PR64. At NGC, the population follows a similar pattern, but NGC reports one PR67CAM (the Kaufman Collection coin) and one PR68CAM as finet known.
Cameo examples comprise a small percentage of the total Proof mintage. Deep Cameo examples may not exist at all, as none have been certified in any grade.