A new grad and already on the Layoff. Not a good start :) I've had the pleasure to work with a bunch of EICs and what they lack in experience, they make up for in appetite and general interest. You'll meet plenty of people in Cisco doing a phone it in performance, be they seasoned or EIC.
The advice goes works for any company. It's important to consider where you see yourself in 2-5 years. Are you an engineer that sees themselves more in the field, more in the area of coordination or specializing in SW. I know most engineers dread that question, in interviews, but its worthwhile to consider it, as will Cisco help toward that end goal or hinder it. Think of this like chess, you gotta consider your strategy beyond 1 move.
Also, consider the type of engineer you are. Are you a HW or SW person. If you're SW, I'd advise regardless to steer well clear of Cisco and I've not as yet come across anyone whos knows anything about SW, much less building great teams. That being said, Cisco is massive and maybe, just maybe theres a stellar SW team out there, so consider the team, what you'll be doing. Where are your team located? Are they in Morgan Hill and Pleasanton, in which you'll never see them? Or are they a tight knit group, who collaborate(not via Webex or Jabber garbage) and do you see yourself getting better in their company. What about the field they work in, does this interest you? What about yourself, do you value benefits and stability or making a difference and being a net contributor?
Truly most of these questions apply regardless of Cisco and you can always be LR'ed almost everywhere, the only difference is the length of the process to do so and the comfort of the parachute. You're at the start of your career, the world is your oyster, embrace it!