A few thoughts:
Sam Bradford is the starter. Tebow would not compete for the starting quarterback's job in St. Louis. The Rams are committed to Bradford for at least the 2012 season and most likely beyond, barring a dramatic change in thinking brought about by unforeseen developments.
Backup market thinning. Shaun Hill and Brady Quinn signed contracts elsewhere after visiting the Rams. Kellen Clemens finished last season with the Rams and played for new offensive coordinator Brian Schottenheimer when the two were with the Jets. Clemens remains an unrestricted free agent. The Rams are considering other options.
Tebow's name recognition. Let's face it, the Rams have lacked relevance in recent years. They have virtually no star power beyond Steven Jackson. Tebow would become at least a curiosity. The Rams could find ways to use him as a runner or in certain packages. Adding Tebow could change the subject away from the recently suspended Gregg Williams, as well.
Protecting John Elway. Getting Manning allowed the Denver Broncos to dump Tebow without incurring much fallout from Tebow's large and passionate fan base. Setting up Tebow for failure in the future would further insulate the Broncos from criticism if the Manning acquisition doesn't produce the desired results. Jets fans would be quick to chant for Tebow and also quick to boo him at the first sign of failure. And in St. Louis, Bradford's presence would block Tebow from the lineup for the foreseeable future.
That's it for now. ESPN's Adam Schefter says Tebow still might be headed to the Jets. The sides are working through elements related to Tebow's contract.
Note: The Rams have not made an offer for Tebow, according to Jim Thomas of the St. Louis Post-Dispatch.
Update: Rams sources are denying any interest in Tebow, according to Thomas.