That's assuming there are no alternative offers other than the Rams.
There's a short list of teams that can make alternative offers. Cleveland has McCown and Manziel. If they're going QB, it's in the draft. The 49ers could go QB in FA but it makes more sense for them to use the draft. The Texans might go QB but they also might opt to stick with Hoyer and I doubt the QBs we'd be interested in would strike their fancy. Jets are likely to re-sign Fitzpatrick. Who knows what the Eagles are doing. But they could be competition if they let Bradford walk. Broncos may or may not be competition depending on what they do with Osweiler. Redskins will keep Cousins.
That leaves us with maybe two to four teams that can offer a chance to compete with the starting job.(San Francisco [more likely to use the draft], Texas [unlikely to pursue guys like Kaep and Daniel], Denver {will depend on Osweiler], and Philly [will depend on Bradford])
There's also a possibility that the number could be one or zero. Which would mean we'd be offering a starting job while other teams are offering backup jobs.