It depends on if you denominate "large" in bytes or dollar cost. If the former, then nothing; the blockchain will inexorably become impossibly large (which is good!). If the latter, then the exponentially decreasing price of storage costs will counter blockchain growth.
That assumes an infinite moores law.
This faces 2 issues:
1. Physics, you just can't continue shrinking infinitely and the cost of shrinking are growing exponentially driving competition out of the market.
2. Market, SSDs have shifted focus to speed over size while being very expensive; companies are leaving the HDD market as well as consolidating. Fewer players means higher costs.
