Given that localStorage only has 5MiB available to it, you could try using the localForage library to have a localStorage-like API around IndexedDB, so that people can store even larger notes (you could even support storing pasted images as PNG blobs). Even better: is has automatic localForage fallback.
Alternatively, you might want to either compress the text with LZ-String before storing it[1]. (BTW, version 2.0 is currently in the works and much faster, especially if you use the "Unsafe" version[2])
[0] https://localforage.github.io/localForage/
[1] http://pieroxy.net/blog/pages/lz-string/index.html
[2] https://github.com/pieroxy/lz-string/pull/98#issuecomment-40...