Detroit is currently 8 points behind Pittsburgh, with 2 games in hand. Based on points per game played, the Wings are on pace to finish 11 points out of the Wild Card (80 vs 91).
While nobody in the middle of the Eastern Conference standings is setting the league on fire, there are likely too many teams to climb past before the trade deadline. Which should lead to selling Green. Which should widen the gap between Detroit and the field.
Realistically, I think their path is already set, barring a statistically unlikely stretch of play (both Detroit winning and several others losing). But over half a season of .500 hockey is a pretty good indicator that the current roster isn't about to start tearing it up, at least not with any consistency.
EDIT: For perspective, based on the percentage of their current points coming from losses in OT or the shootout (and then adding one, since otherwise they'd need one extra point from a win), the Wings would need to go 21-10-7 to make the Wild Card, assuming status quo for the rest of the East.