It's hard enough getting the pieces for a 34 defense, but the hard ones are the 2 5 techs (34 DE) and 1 0 tech (NT). Then you need man coverage corners (because of the blitzing schemes), they're a better zone team (last time I looked... a few years back).
Who do you take with their 1st pick (currently 3rd) to fill those needs. Gerald McCoy is likely the top player available for any of those positions. Do you reach and get Joe Haden? Eric Berry and play a safety bound 34 D? Obviously, you want to trade down to the middle of the round.
Then their second pick is out of range for a NT (in my opinion) without trading up (which is bad for a team that sucks). A 34 DE is possible there (because half of my board at that point is people who could be 5-techs).
You keep going and you finally see to get the players for the defense, you'll have to spend like 80 % of your draft and hope some people want to play in warm weather and domes... because otherwise, you have little to no hope of FAs.
They need to use what they have there. They won't have the luxury to sign players to fill positions and drafting them will be tough.