So, with the Alex Smith trade, we now have exactly 80 guys on the roster. To sign anyone else to a contract (like Jason Taylor or a tryout contract guy), we'd have to cut someone now on the roster. Griese? We aren't likely to get anything for him...
The draft picks don't count against the 80 until they sign their contracts, so conceivably we can carry more throughout the summer until just before training camp when the draftees usually sign.