It is not a limitation on the browser side. Read RFC2109 which states cookie limitations.
6.3 Implementation Limits
Practical user agent implementations have limits on the number and
size of cookies that they can store. In general, user agents' cookie
support should have no fixed limits. They should strive to store as
many frequently-used cookies as possible. Furthermore, general-use
user agents should provide each of the following minimum capabilities
individually, although not necessarily simultaneously:
* at least 300 cookies
* at least 4096 bytes per cookie (as measured by the size of the
characters that comprise the cookie non-terminal in the syntax
description of the Set-Cookie header)
* at least 20 cookies per unique host or domain name
You best bet is to store the data in your db and then you can save your data id / key in the cookie.