I found some interesting research from Draftmetrics that may make you think twice about the need for the Eagles to pick a LB in the first round of this years' draft. The site broke down the percentage of starts made by every player according to the round they were drafted in. Here's what they found about linebackers.
There has been a recent trend for an increasing percentage of starts by undrafted free agents, 12% in 2005 and 2006 increasing to 18% in 2011. This was preceded by a big drop from a peak of 27% in 1995 to 11% in 20003
Linebackers join offensive linemen and tight ends in the fewest starts from first and second round picks. The percentage of starts from third and fourth round picks has been on a decline. Over 30% from 1992 through 2007, then dropped off to a low of 19% in 2010
They found that over the last 10 years, only 23% of the starts at LB were made by first round picks. Undrafted free agents actually made 14% of the starts. The draft is still all about individual player evaluation, so I don't think this research would discourage a team from taking a LB in the first round, but it does show that relative to other positions, starting LBs really can be found later.
Of course, this does beg the question, if LBs appear to be so abundant in the later rounds... Why have the Eagles not hit on at least one with all the picks they've made? For the full research report check out this PDF.