From RFC 2068 (HTTP/1.1):

The HTTP protocol does not place any a priori limit on the length of a URI. Servers MUST be able to handle the URI of any resource they serve, and SHOULD be able to handle URIs of unbounded length if they provide GET-based forms that could generate such URIs. A server SHOULD return 414 (Request-URI Too Long) status if a URI is longer than the server can handle (see section 10.4.15).

Apache allows you to change this. From http://httpd.apache.org/docs/mod/core.html#limitrequestline:

The LimitRequestLine directive allows the server administrator to reduce the limit on the allowed size of a client's HTTP request-line below the normal input buffer size compiled with the server.

This page says that Apache's limit is 8190 by default, so I don't think it's the server. In my experience, a 1024 byte limit is generally because of the browser. Are you using IE? I seem to remember having some unexpected problems once because I was testing in Netscape and IE users couldn't use the form properly.

So, as has already been suggested, use POST instead.

update: wait - you said 1.5K of text. I still think it's the browser though.