Having released Trent Green, the Rams have Brock Berlin penciled in at the backup quarterback spot. They've made no effort to replace him as of yet, though the list of available free agents includes Kerry Collins and Jeff Garcia.
If the Rams want to bypass the free agent market, then thye must pursue the college route. I would like to make a case for Mike Teel of Rutgers as a possible second-day pick. Look at his following stats:
He also has four bowl appearances, and won three of them.
In 2008, he led the Scarlet Knights to an 11-1 record and a victory in the Papajohns.com Bowl over North Carolina State. I know, Papajohns.com isn't a big name (and none of their other bowl appearances have been in big-name games), but it's the fact that rutgers is playing in the postseason that should be taken into account.
Still, I think the best scenario would be to release Brock Berlin, bring in a free agent, and draft someone like Teel in the later rounds. By signing someone like a Collins or a Garcia, you have an able backup for Bulger and time for your rookie to develop.
Also, keep in mind that Bulger has two concussions. A third one might force him to retire. It would be better in the long-term for the team to have an experienced backup should worst come to worst.