Yes, I think the Philadelphia Eagles are in trouble now with so many injuries. I think they are in trouble when most of their players are injured. If their players can't play then I think they'll have a hard time winning with their back ups playing for their injured players.
Anytime you have multiple injuries on any team it seriously underminds your ability to play top-notch games. The more injuries a team experiences the more second and third string guys fill in for the premium players. Second and third string players are still talented athletes but they have not had the time or experience of play as the premium player.
Are injuries ideal? No, of course not and while many lesser teams who overly rely on a single star player may fold, a team of depth and skill can overcome. The team has experienced players and a significant cushion of results and strong management should be sufficent to survive this period albeit not thriving as they might have without the injuries.
One of the major factors that coaches and general managers have to take into account when building and managing their teams is the inevitability that their players will get injured playing high level competitive sports. If the Eagles end up doing poorly, it isn't their injured players' faults so much as a lack of planning beforehand.