Yeah, it could happen. At 6-8 the Rams are outside looking in. The Eagles, right now, are in the first Wild Card spot at 8-6. At 7-7, the Giants and the Falcons are on tenuous ground in a tie for the second WC spot.
For anything to happen, the Rams must win their last two games of the season. Beating the Redskins and the Vikings won't be an easy task, but it's not entirely outside the realm of possibility.
Some other chips have to fall in the right place too.
The Giants and the Falcons have to lose both of their remaining games. The Giants face New Orleans this week and Washington next. The Falcons face Carolina and Philly in their final two games.
Should those two teams fall by the wayside with 0-2 records to finish the season, a couple other things have also have to happen in order to prevent one of the other 6-8 teams from grabbing that final WC spot. The Niners, whom have beaten the Rams twice, must lose at least one of their next two games against Arizona and Denver; otherwise, at 8-8 they would win out for the WC spot over the Rams based on their head-to-head and divisional record. The other 6-8 teams - Carolina, Minnesota, and Green Bay - also have to lose at least one of their final two games.
It's not the best scenario for the Rams, all things considered. The only factor that the Rams have any control over is winning their next two games. More importantly, a 3-0 run to end the season would ease some painful memories and give fans a little hope for next season.
For a good rundown of the playoff scenarios for the entire league, be sure to see this post at Cincy Jungle.